Algebra Basics - Solving Basic Equations - Quick Review!

Summary

This video provides a clear and comprehensive introduction to solving basic equations, focusing on techniques such as isolating variables, using inverse operations for addition and subtraction, and applying multiplication and division. The presenter walks through several examples, illustrating how to approach various equations, including those with fractions and multi-step problems. Viewers are encouraged to verify their solutions, reinforcing understanding through practice. Overall, the video serves as a practical guide for anyone looking to grasp the fundamentals of algebraic equations.

Takeaways

• 😀 Basic equations can be solved by isolating the variable, often represented as x.
• 😀 The opposite of addition is subtraction; to isolate x, you often need to subtract from both sides of the equation.
• 😀 When given an equation like x + 4 = 9, you can find x by performing inverse operations.
• 😀 To verify solutions, substitute the found value back into the original equation.
• 😀 When solving x - 5 = 6, you add 5 to both sides to isolate x.
• 😀 For multiplication equations like 3x = 24, divide both sides by the coefficient to find x.
• 😀 In division equations such as x ÷ 4 = 5, multiply both sides by the divisor to solve for x.
• 😀 Cross multiplication can be used when solving equations involving fractions.
• 😀 Multi-step equations require you to perform operations in a sequence to isolate x.
• 😀 Always check your work by substituting the solution back into the original equation to ensure accuracy.

Q & A

What is the first step to solve the equation x + 4 = 9?

The first step is to subtract 4 from both sides of the equation, leading to x = 9 - 4, which simplifies to x = 5.

How do you isolate the variable x in the equation x - 5 = 6?

To isolate x, add 5 to both sides of the equation, resulting in x = 6 + 5, which simplifies to x = 11.

In the equation 5 - x = 7, how do you solve for x?

First, subtract 5 from both sides, giving -x = 7 - 5, which simplifies to -x = 2. Then, multiply both sides by -1 to get x = -2.

What operation do you perform to solve the equation 3x = 24?

You divide both sides by 3, which gives x = 24 / 3, leading to x = 8.

How do you handle the equation x / 4 = 5 to find x?

To solve for x, multiply both sides by 4, resulting in x = 5 * 4, which simplifies to x = 20.

What technique is used to solve the equation 12 / x = 4?

You can use cross-multiplication: 12 * 1 = 4 * x, which simplifies to 12 = 4x. Then divide both sides by 4 to find x = 3.

In a multi-step equation like 3x + 2 = 14, what is the first action to take?

The first action is to subtract 2 from both sides, resulting in 3x = 14 - 2, which simplifies to 3x = 12.

After isolating 3x in the equation 3x = 12, how do you find the value of x?

You divide both sides by 3, leading to x = 12 / 3, which simplifies to x = 4.

What verification method is suggested to ensure the solutions are correct?

The verification method involves substituting the value of x back into the original equation to check if both sides are equal.

What is the importance of performing the opposite operation when solving equations?

Performing the opposite operation helps to isolate the variable on one side of the equation, which is essential for finding its value.