Solving Two-Step Equations | Algebra Equations
Summary
TLDRIn the 'Math with Mr. J' video, the focus is on solving two-step equations. Mr. J demonstrates how to isolate variables by reversing operations, ensuring equation balance. Examples include undoing subtraction and division to isolate 'x' in '2x - 6 = 10', leading to x = 8, and 'R/5 + 8 = 11', resulting in R = 15. The video also covers handling parentheses and variables on different sides of the equation, emphasizing the importance of checking solutions in the original equations.
Takeaways
- 🔢 The main goal in solving equations is to isolate the variable.
- ⚖️ To maintain balance, whatever operation is done to one side of the equation must be done to the other side.
- 🔄 The process involves reversing the order of operations to isolate the variable.
- ➕ To eliminate subtraction on one side, add the opposite on both sides.
- ➗ To remove multiplication, use division as the opposite operation.
- 🔄 For equations like '2x - 6 = 10', first add 6 to both sides to eliminate the subtraction, then divide by 2 to solve for x.
- 🔄 In equations with division and addition, such as 'r/5 + 8 = 11', subtract 8 from both sides first, then multiply by 5 to solve for r.
- 🔄 When the variable is on the right side, like in '7 = 16 - 3e', subtract the constant from both sides to move the variable to the left.
- 🔄 Parentheses can be handled by dividing both sides by the coefficient outside the parentheses to simplify the equation.
- 🔄 Always check the solution by plugging the isolated variable back into the original equation to ensure accuracy.
Q & A
What is the main goal when solving equations with variables?
-The main goal is to isolate the variable, getting it by itself to solve the equation.
Why is it important to perform the same operation on both sides of an equation?
-It is important to perform the same operation on both sides to keep the equation balanced.
In the first example, what is the first step to isolate the variable 'x'?
-The first step is to add 6 to both sides of the equation to eliminate the subtraction of 6 on the left side.
How does adding 6 to both sides of the equation 2x - 6 = 10 help in solving for x?
-Adding 6 to both sides results in 2x = 16, which simplifies the equation and brings us closer to isolating x.
What is the reverse operation of multiplication used in the script?
-The reverse operation of multiplication is division, which is used to isolate the variable by making the coefficient equal to 1.
For the equation R / 5 + 8 = 11, how do you reverse the operation of addition?
-To reverse the addition, you subtract 8 from both sides of the equation to isolate the term with the variable R.
What is the purpose of multiplying both sides of an equation by 5 when solving for R in the equation R / 5 + 8 = 11?
-Multiplying both sides by 5 reverses the division by 5, which helps to isolate the variable R.
In the equation 7 = 16 - 3e, how do you handle the negative sign in front of the variable?
-You divide both sides by -3 to isolate the variable e, reversing the multiplication by -3.
Why is it necessary to divide both sides by 2 in the equation 2(y - 8) = 24?
-Dividing both sides by 2 undoes the multiplication by 2 outside the parentheses, simplifying the equation to y - 8 = 12.
How does adding 8 to both sides of the equation y - 8 = 12 help in isolating y?
-Adding 8 to both sides cancels out the -8 on the left side, leaving y by itself on the left side of the equation.
What is the final step to verify the solution to an equation?
-The final step is to plug the solution back into the original equation to see if it satisfies the equation and yields the correct result.
Outlines
📘 Solving Two-Step Equations
This segment of the video introduces the concept of solving two-step equations with Mr. J. The process involves isolating the variable to solve the equation, ensuring that any operation performed on one side of the equation is mirrored on the other to maintain balance. The video demonstrates this with the equation 2x - 6 = 10, where Mr. J reverses the operations by first adding 6 to both sides to eliminate the subtraction, and then dividing by 2 to isolate x, resulting in x = 8. The solution is verified by substituting the value back into the original equation.
📗 Advanced Two-Step Equation Techniques
In the second part, the video script delves into more complex two-step equations, such as R/5 + 8 = 11 and 7 = 16 - 3e. The method involves reversing the operations to isolate the variable. For R/5 + 8 = 11, Mr. J subtracts 8 from both sides and then multiplies by 5 to solve for R, finding R = 15. For 7 = 16 - 3e, the script shows subtracting 16 from both sides and then dividing by -3 to solve for e, resulting in e = 3. Each solution is checked by substituting the found value back into the original equation to confirm its correctness.
Mindmap
Keywords
💡Two-step equations
💡Isolate the variable
💡Reverse order of operations
💡Balanced equation
💡Subtraction
💡Division
💡Multiplication
💡Parentheses
💡Variable
💡Coefficient
Highlights
Introduction to solving two-step equations.
Goal of isolating the variable in an equation.
Principle of maintaining equation balance by performing the same operation on both sides.
Solving the first equation: 2x - 6 = 10 by reversing operations.
Adding 6 to both sides to eliminate the -6 on the left side.
Dividing both sides by 2 to isolate x.
Verification of the solution x = 8 by plugging it back into the original equation.
Solving the second equation: R/5 + 8 = 11 using reverse order of operations.
Subtracting 8 from both sides to isolate R/5.
Multiplying both sides by 5 to solve for R.
Verification of the solution R = 15 by checking the original equation.
Approach to solving equations with variables on the right side, such as 7 = 16 - 3e.
Eliminating the constant 16 by subtracting 16 from both sides.
Dividing both sides by -3 to isolate e.
Verification of the solution e = 3 by substituting it into the original equation.
Handling equations with parentheses, like 2(y - 8) = 24.
Dividing both sides by 2 to eliminate the multiplication outside the parentheses.
Adding 8 to both sides to isolate y.
Verification of the solution y = 20 by plugging it back into the original equation.
Summary of the method for solving two-step equations.
Transcripts
welcome to math with mr. J in this video
I'm going to cover how to solve two-step
equations we have for example problems
on your screen there that we're going to
go through together in order to get this
down now remember when we have an
equation with a variable our goal is to
isolate that variable or get it by
itself in order to solve and we also
need to remember whatever we do to one
side we must do to the other side of the
equation we have to keep it balanced so
let's jump right into the number one and
solve some two-step equations so for
number one we have 2x minus 6 equals 10
so again we want to isolate that X get
it by itself so I like to think of it as
we need to reverse the order or undo
this side of the equation so we get that
X by itself and we're going to use the
reverse order of operations in order to
do so so we have 2 times that X and then
we subtract a 6 so reverse order of
operations this subtraction of 6 needs
to come first so how do we get rid of
that 6 from the left side well we can
add 6 that will cancel those sixes out
or give us a 0 so remember whatever we
do to one side we have to do to the
other so if we add 6 to the left we need
to add 6 to the right a negative 6 or
minus 6 plus 6 gives us that 0 and 10
plus 6 is 16 so on the left side we're
left with 2 times X or 2x so we don't
have the variable completely isolated
yet but we're almost there so we have 2
times X so how do we get rid of that 2
we need to either make it a 0 or a 1 so
the opposite of multiplying by 2 would
be dividing by two that would give us
one X on that side which is the same as
just X so let's divide both sides by two
and that leaves us with x equals 16
divided by 2 is 8 now let's plug in that
8 into the original original equation
and see if we get the correct answer so
2 times 8 minus 6 equals 10 it's always
a good idea to see if that answer works
out 2 times 8 is 16 minus 6 does give us
that 10 so we have the correct answer x
equals 8 so for number two we have R
divided by 5 plus 8 equals 11 so we need
to get that R by itself so let's do the
reverse order of operations to undo the
left side of the equation so let's get
rid of that 8 first so we have plus 8 so
the opposite let's subtract 8 from both
sides to begin to isolate the R so a
positive 8 and a negative 8 there minus
8 gives us zero and 11 minus 8 gives us
3 so on the left side we're left with R
divided by 5 so let's get rid of the 5
from the left side what's the opposite
of divided by 5 dividing by 5 well
multiplying by 5 so let's multiply both
sides by 5 by 5 by 5 and we get R equals
well 3 times 5 is 15 we isolated the
variable and it equals 15 so on the left
hand side I just want to mention we had
R divided by 5 that last step and we
times by 5 which would technically give
us R over 1 or
are divided by one which is just our
this is isolating the variable right
here if you get to multiplying that
variable by one or dividing that
variable by one so let's plug in that 15
and see if we get the correct answer
here so I'm running out of room a little
bit I'll fit it in here so 15 divided by
5 is 3 bring down an hour 8 and we end
up with 3 plus 8 which gives us the 11
we want it so let's go over to number 3
here where we have 7 equals 16 minus 3e
so the equation looks a little different
than numbers 1 & 2 we have the variable
on the right-hand side but it's the same
exact thing that we did for numbers 1 &
2 so we need to isolate that e so undo
that right side of the problem so let's
get rid of the 16 first so we have a
positive 16 on the right hand side so
the opposite would be subtracting 16 in
order to get rid of it let's do minus 16
on the left hand side as well so 16
minus 16 gives us at 0 7 minus 16 gives
us a negative 9 we're left with negative
3 e on the right side so that's
multiplication so we need to do the
opposite of multiplication in order to
get the e by itself so let's divide both
sides by negative 3 negative 9 divided
by negative 3 gives us a positive 3 and
we're left with E over 1 which is the
same thing as just E we isolated the
variable so e equals 3 let's plug it
back in and see if that works
three times three is nine
bring down our 16 16 minus nine does
give us that seven that we are looking
for on the left-hand side of that
equation so we were correct e equals
three and lastly number four so we have
some parentheses in this one and we need
to get Y by itself or isolate the
variable Y so we have two times
parenthesis Y minus eight and
parenthesis equals 24 so we need to do
the opposite remember we need to undo
that side the left-hand side of the
equation and we're going to actually
divide both sides by two to undo that
two that is outside of the parenthesis
so two divided by two is one that gives
us one outside of the parenthesis there
which is just going to leave us with y
minus eight because anything times one
is just that number or expression itself
so we just have Y minus eight and then
24 divided by two is 12 so now we have Y
minus 8 equals 12 so we need to get rid
of that minus eight undo that part of
the left hand side of the equation in
order to isolate the Y so we need to add
8 to both sides in order to isolate the
Y so a minus 8 and a plus 8 gives us a 0
those cancel out so we're left with Y
and 12 plus 8 gives us 20 so y equals 20
let's plug it back into the equation to
see if this gives us the answer 24 that
we're looking for
20 minus 8 is 12 bring down the 2
outside of the parentheses which means
multiplication and 2 times 12 does give
us that 24 that we wanted so there you
have it there's how you solve two-step
equations hopefully that helped thanks
so much for watching
until next time peace
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