1.6 Equations with Variables on Both Sides

Fill in the Blanks

Use inverse operations to collect ____________ on the same side of the equation. Use inverse operations to collect ____________ on the opposite side of the equation. ____________ the equation by isolating the variable.

Multiple Choice

Which of the following is the correct first step to solve the equation 8x - 7 = 4x + 21?

• Subtract 4x from both sides

• Add 7 to both sides

• Divide both sides by 8

• Subtract 21 from both sides

Multiple Select

Select all equations that have variables on both sides.

• 8x - 7 = 4x + 21

• x + 5 = 10

• -11x + 9 = -2x + 45

• y = 2y + 3

Fill in the Blanks

Solve the equation: 13x + 9 = 6x - 12. What is the value of x?

Multiple Choice

What is the value of x that makes the equation (1/4)x + 17 = x - 4 true?

• 28

• -28

• 21

• -21

Fill in the Blanks

Solve for x in the equation 3(2x + 1) = 5(x - 4).

Multiple Select

Which of the following steps is necessary to solve the equation 6 + 12(x + 3) = 7x + 30 + 6x?

• Distribute 12 to (x + 3)

• Combine like terms on both sides

• Subtract 6 from both sides first

• Divide both sides by 12 first

Multiple Choice

Brayden and Ellie each solved an equation. Who solved their equation correctly?

• Brayden

• Ellie

• Both

• Neither