Solving Linear Equations and Verification

The video tutorial explains how to solve a linear equation in one variable by isolating the variable, distributing terms, and simplifying the equation. It demonstrates the process of solving a multi-step equation, including distributing, adding, and subtracting terms to isolate the variable. The tutorial also covers simplifying fractions and verifying the solution by substituting it back into the original equation. The explanation is clear and methodical, ensuring that the solution satisfies the equation.

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

• To eliminate all variables

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

• To convert the equation into a quadratic equation

• To find the sum of all coefficients

In the equation 3(2x - 5) = -30, what is the first step to simplify it?

• Multiply both sides by 2

• Distribute the 3 across the terms inside the parentheses

• Add 5 to both sides

• Divide both sides by 3

What does the equation 3(2x - 5) = -30 classify as?

• A polynomial equation

• A single-step equation

• A multi-step equation

• A quadratic equation

When distributing, how is subtraction treated?

• As adding a negative

• As a division

• As a positive term

• As a multiplication

What operation is used to isolate the variable term 6x in the equation 6x - 15 = -30?

• Divide both sides by 6

• Subtract 15 from both sides

• Add 15 to both sides

• Multiply both sides by 6

What is the final step to solve for x in the equation 6x = -15?

• Multiply both sides by 6

• Subtract 6 from both sides

• Add 6 to both sides

• Divide both sides by 6

What is the simplified form of the fraction -15/6?

• -5/3

• -5/2

• -2/5

• -3/2

How do you verify the solution of a linear equation?

• By substituting the solution back into the original equation

• By graphing the equation

• By solving a different equation

• By checking the solution with a calculator

What is the result of substituting x = -5/2 into the original equation 3(2x - 5) = -30?

• The left side equals -25

• The left side equals -30

• The left side equals 0

• The left side equals 5

What is the purpose of simplifying the left side of the equation during verification?

• To change the equation type

• To confirm the solution satisfies the equation

• To ensure the solution is incorrect

• To make the equation more complex