Solving Linear Equations and Verification

This video tutorial explains how to solve linear equations in one variable, focusing on simplifying equations and using the multiplication or division property of equality. It provides two examples: one without parentheses and another with parentheses, demonstrating the process of simplifying and solving each equation. The video also verifies the solutions by substituting the values back into the original equations.

What is the primary goal when solving a linear equation in one variable?

• To find the value of the variable that makes the equation true

• To eliminate all variables from the equation

• To convert the equation into a quadratic equation

• To ensure both sides of the equation are identical

In the first example, what is the result of combining the like terms on the left side of the equation?

• 64

• Negative 100

• 28

• 0

How do you isolate the variable x in the equation 28 = 7x?

• Add 7 to both sides

• Divide both sides by 7

• Subtract 7 from both sides

• Multiply both sides by 7

What is the purpose of substituting the solution back into the original equation?

• To simplify the equation further

• To change the equation's form

• To verify the solution is correct

• To find a different solution

In the second example, what operation is used to simplify the left side of the equation?

• Addition

• Subtraction

• Division

• Distribution

What is the simplified form of the left side of the equation in the second example after distribution?

• Negative 2x

• Zero

• Negative 8

• 16

How do you solve for x in the equation -2x = 16?

• Multiply both sides by -2

• Add 2 to both sides

• Divide both sides by -2

• Subtract 2 from both sides

What is the solution to the equation -2x = 16?

• x = -8

• x = 8

• x = -16

• x = 16

Why is it important to verify the solution by substituting it back into the original equation?

• To confirm the solution satisfies the equation

• To ensure the solution is unique

• To simplify the equation further

• To find alternative solutions

What is the result of substituting x = -8 back into the original equation of the second example?

• The equation remains unchanged

• The equation becomes false

• The equation is verified as true

• The equation simplifies to zero