4 Steps to Solving Multi-Step Inequalities | 7.EE.B.4 💚
Summary
TLDRIn 'The Magic of Math' video, the host teaches how to solve multi-step inequalities using four key steps: clear parentheses, isolate the variable, get a coefficient of one, and graph the solution. The tutorial employs prior knowledge of equations to guide viewers through examples, emphasizing the importance of maintaining inequality properties throughout the process. The lesson aims to make mastering math approachable and engaging.
Takeaways
- 📘 The lesson focuses on solving multi-step inequalities, which requires understanding and applying prior knowledge of solving equations and inequalities.
- 🔍 There are four key steps to solving multi-step inequalities: clearing parentheses, isolating the variable term, simplifying the variable to a coefficient of one, and graphing the solution.
- 👉 Step one involves using the distributive property to clear parentheses if necessary.
- 🔄 Step two circles the variable term and adds or subtracts values from both sides to isolate the variable.
- 🔄 Step three circles the variable and involves multiplying or dividing by a value to simplify the variable's coefficient to one.
- 📊 Step four is graphing the solution on a number line, using appropriate symbols for the inequality type (e.g., open or closed circles).
- ⚠️ It's important to remember that operations in front of terms can indicate whether they are positive or negative, affecting the direction of the inequality.
- ➗ When dividing both sides of an inequality by a negative number, the inequality symbol must be reversed.
- 📐 The process includes creating 'zero pairs' to isolate the variable term, which involves performing the inverse operation to what is already present.
- 📈 The video provides examples of solving inequalities with different operations, emphasizing the need to maintain the properties of equality when manipulating both sides of an inequality.
- 📚 The lesson encourages viewers to practice solving inequalities by pausing the video and attempting the problems themselves, then checking their work against the provided solutions.
Q & A
What is the main topic of the 'Magic of Math' video?
-The main topic of the video is solving multi-step inequalities.
What are the four steps to solving multi-step inequalities as outlined in the video?
-The four steps are: 1) Clear parentheses by performing the distributive property if necessary, 2) Circle the variable term and add or subtract a value from both sides to isolate it, 3) Circle the variable and multiply or divide a value from both sides to get a coefficient of one, and 4) Graph the solution.
Why might steps one and two not be necessary when solving multi-step inequalities?
-Steps one and two might not be necessary if the inequality does not have parentheses that require clearing or if the variable term is already isolated.
What is the end goal when solving for the variable in an inequality?
-The end goal is to have the variable with a coefficient of one, so you can determine what the variable is less than, greater than, or equal to.
How does the video suggest handling negative values when solving inequalities?
-When multiplying or dividing by a negative value, you must reverse the inequality symbol to maintain the correct relationship.
What symbol should be used on a number line to represent a value that the variable can be equal to?
-A closed circle should be used on the number line to represent a value that the variable can be equal to.
What symbol should be used on a number line to represent a value that the variable cannot be equal to?
-An open circle should be used on the number line to represent a value that the variable cannot be equal to.
How does the video suggest identifying the variable term in an inequality?
-The video suggests identifying the variable term by looking at what operation is applied to it and noting whether it's positive or negative.
What is the purpose of creating a 'zero pair' when solving inequalities?
-Creating a 'zero pair' is done to isolate the variable term by eliminating the constant that is added or subtracted from it.
What should you do when you encounter parentheses in an inequality that requires solving?
-When encountering parentheses, you should perform the distributive property to clear them before proceeding with the other steps.
How does the video demonstrate the process of solving a multi-step inequality?
-The video demonstrates the process by walking through several examples, showing each step from isolating the variable to graphing the solution on a number line.
Outlines
📚 Introduction to Solving Multi-Step Inequalities
The script begins with an introduction to a lesson on solving multi-step inequalities, emphasizing the connection between solving equations and inequalities. The instructor outlines a four-step process to tackle these problems: clearing parentheses, isolating the variable term, simplifying the variable to have a coefficient of one, and graphing the solution. The lesson encourages students to apply prior knowledge and introduces the concept of zero pairs and the importance of maintaining the properties of equality when manipulating inequalities.
🔍 Detailed Steps and Examples for Solving Inequalities
This paragraph delves into the specifics of solving multi-step inequalities with detailed examples. It covers the process of eliminating parentheses, if present, and then isolating the variable term by creating zero pairs. The instructor demonstrates how to reverse operations to simplify the inequality, such as dividing by a negative number, which requires flipping the inequality sign. Each example is followed by a step to graph the solution set on a number line, using open or closed circles to indicate inclusivity or exclusivity of the endpoint, and shading the appropriate region to represent the solution set.
📈 Final Steps and Conclusion of the Lesson
The final paragraph wraps up the lesson by summarizing the four steps for solving multi-step inequalities and encouraging viewers to practice these steps. It includes a reminder to apply the steps to all types of inequality symbols. The instructor thanks the viewers for joining the 'Magic of Math' and invites them to subscribe for more educational content. The lesson concludes with a friendly sign-off, wishing viewers a great day and expressing hope for their return to the channel.
Mindmap
Keywords
💡Multi-step Inequalities
💡Distributive Property
💡Variable Term
💡Coefficient
💡Zero Pair
💡Inequality Symbol
💡Graphing Solution
💡Number Line
💡Closed Circle
💡Open Circle
💡Master Math
Highlights
Introduction to solving multi-step inequalities using prior knowledge of equations and inequalities.
Four-step process for solving multi-step inequalities: clear parentheses, circle variable terms, isolate the variable, and graph the solution.
Step one involves using the distributive property if necessary to clear parentheses.
Step two focuses on isolating the variable term by adding or subtracting values from both sides of the inequality.
Step three circles the variable and adjusts coefficients to achieve a coefficient of one.
Step four involves graphing the solution on a number line, noting the type of inequality symbol.
Demonstration of solving an inequality with no parentheses and isolating the variable term.
Explanation of creating a zero pair to isolate the variable and the inverse operation of subtraction.
Isolating x by dividing by the coefficient, maintaining the properties of equality.
Graphing the solution with a closed circle on the number line for 'greater than or equal to'.
Solving an inequality with a negative coefficient and reversing the inequality symbol when multiplying by a negative.
The importance of remembering to reverse the inequality symbol when dealing with negative values.
Another example of solving an inequality, emphasizing the process of creating a zero pair and isolating the variable.
Dividing by a negative number and reversing the inequality symbol to find the solution.
Graphing the solution with an open circle on the number line for 'less than'.
Invitation for viewers to pause the video and practice solving an inequality with provided steps.
Review of solving an inequality with distribution, emphasizing the process of zero pairing and isolating the variable.
Final demonstration of solving and graphing an inequality, including dividing by the variable's coefficient.
Conclusion summarizing the four-step process for solving multi-step inequalities.
Transcripts
hi welcome to the magic of math where we
master math one video at a time
today my lesson is on solving multi-step
inequalities
our objective today is just that we will
solve multi-step inequalities but here's
what i would like you thinking about as
i proceed through the lesson today
how can you use what you already know
about solving equations and inequalities
to solve multi-step inequalities
so we're going to draw on your prior
learning
there are four steps to solving
multi-step inequalities step one
if necessary clear parentheses by
performing the distributive property
step two
circle the variable term
and if necessary add or subtract a value
from both sides of the inequality to
isolate the variable term
reminding you that steps one and two may
or may not be necessary
step three circle the variable if all
that's on the left or the right of the
inequality symbol is the variable term
circle the variable
then if necessary multiply or divide a
value from both sides of the inequality
so the variable has a coefficient of one
so this is our end goal we want to know
what the variable is less than greater
than or less than or equal to or greater
than or equal to so the variable needs
to have a coefficient of one
and step four you're going to graph your
solution
noting that this property or these steps
apply to all the inequality symbols less
than greater than less than or equal to
or greater than or equal to
so let's go ahead and dig in and solve a
multi-step inequality so this is called
multi-step because it's going to take
two steps to find the solution set
so the first thing i want to do is there
are no parentheses so i don't need to
distribute but i'm going to isolate this
variable term first so identifying that
my variable term 6x
is being subtracted by 3.
so i need to create a zero pair here so
that i'm left with just 6x on the left
so to do that the inverse of subtract 3
is to add 3 to each side
so this is 0 pair i'm left with 6x
greater than or equal to and 9 plus 3 is
12.
now
i need to get x all by itself i'm going
to isolate x i want a coefficient of 1.
so the inverse of multiply by 6 is to
divide by 6.
what i do to one side of the inequality
i must do to the other to keep the
properties of equality in check
6 divided by 6 is 1 leaving me x
greater than or equal to 12 divided by 6
is 2.
we are ready to graph so i need my
number line i'm going to put my value of
2 on my number line i need a closed
circle because it can be equal to
and it's going to be everything shaded
to the right of two and including two
let's try this one together
again there's no parentheses so i don't
need to distribute so i'm going to
identify my variable term
now i identify that it's being added by
three so i need to create that zero pair
the inverse of add three is to subtract
3 from each side
when i do that i have my variable term
bring down my inequality symbol and 7
subtract 3 is 4.
now i identify what is happening to the
variable
the variable is being divided by
negative four
the inverse of divide by negative four
is to multiply by negative four what i
do to the left i must also do to the
right
now i am multiplying both sides by a
negative value because i am multiplying
both sides by a negative value i have to
remember my rule and reverse the symbol
so it's going to go from greater than 2
less than
so now i'm ready to simplify
negative 4 divided by negative 4 is 1
leaving me x
i already have my symbol
and 4 times negative 4 is negative 16.
there's my solution now we need to graph
i'm going to get my number line i'm
going to put my value negative 16 on my
number line i need an open circle
because it's not equal to
and it's going to be everything shaded
to the left
now it's your turn i would like you to
pause the video now
solve don't forget to graph and come
back when you're done to check your work
welcome back so we're going to identify
our variable term don't forget whatever
operation comes in front of a term
identifies whether it's positive or
negative this is negative 4x
this is positive 3.
so i need to create a zero pair here
this is positive three so i need to
subtract three from each side to create
my zero pair
so bring down the negative four x bring
down the less than or equal to and 27
subtract 3 is 24.
now my variable x i want to create a
coefficient of 1.
so the inverse of multiply by negative
four is to divide both sides by negative
four
i'm dividing by a negative value so i
must make a plan and reverse my
inequality symbol
now i'm ready to simplify
negative 4 divided by negative 4 is 1
giving me just x or 1 x
24 divided by negative 4 is negative 6.
let's graph our solution set
here's my number line
my value negative six on my number line
i need a closed circle because it can be
equal to
and everything shaded to the right
all right your turn again please pause
the video now
solve
graph your solution and come back to
check your work
welcome back
let's go ahead and identify our variable
term
and then it's being added by 13 we're
going to create our zero pair by doing
the inverse and subtract 13 from each
side
this is 0 leaving me 8x
less than or equal to and negative 3 and
negative 13 are negative 16.
now i look to see what's happening to x
x is being multiplied by eight
the inverse of multiplied by eight is to
divide each side by eight
so eight divided by eight is one leaving
the x less than or equal to and negative
sixteen divided by eight
is negative two
we're going to graph our solution we
want negative 2 on our number line we're
going to use a closed circle because it
can be equal to and we're going to shade
to the left
all right here's one that we have to
distribute first
so we're going to three times x and
three times four which is three x plus
twelve
now we're ready to go into step two we
identify our variable term
it's being added by twelve and we want
to create our zero pair so we're going
to subtract 12 from each side
leaving me this is zero 3x greater than
negative 3
9 subtract 12 is negative 3.
identify what's happening to the
variable it's being multiplied by 3 the
inverse of multiplied by 3 is to divide
by 3. what i do to one side i must do to
the other
3 divided by 3 is 1 leaving me x greater
than
negative 1.
our solution on our number line let's
graph our solution set we need a
negative 1 on our number line we want an
open circle because it is not equal to
and it's going to be shaded to the right
now it's your turn i would like you to
pause the video now
solve and graph your solution
welcome back
so we're going to distribute first 7
times x and 7 times negative 2 so that
gives us 7x subtract 14 less than or
equal to negative 21.
we're identifying what's happening to
our variable term and it's being
subtracted by 14. to create my zero pair
here i'm going to add 14 to each side
so this gives us 7x
less than or equal to and negative 21
plus 14 is negative seven
now here's x being multiplied by seven
the inverse would be to divide both
sides by seven
seven divided by seven is one giving me
x less than or equal to
and negative seven divided by seven is
negative one
let's graph our solution set we're going
to plot negative 1 on our number line
we need a closed circle because it can
be less than or equal to
and we're going to shade everything to
the left
and there you have it that is how you
solve multi-step inequalities in four
simple steps i thank you for joining me
today at the magic of math where we
continue to master math one video at a
time i hope you'll come back soon and
subscribe to my channel have a great day
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