Solving Equations with Variables on Both Sides

30 + 6t = 11t

• 3

• 5

• 6

• 30

Jacob solved the following equation using the steps shown.

Step 1 5x + 9 = 2x - 3

Step 2 3x + 9 = -3

Step 3 3x = -12

Step 4 x = -4

What operation did he perform to get from Step 1 to Step 2?

• Subtracted 2x from both sides of the equation

• Subtracted 9 from both sides of the equation

• Multiplied both sides of the equation by 3

• Added -3 to both sides of the equation

10x + 9 = 4x - 9

• 0

• 3

• -3

• -18

What is the solution to the equations?

• one solution

• no solution

• infinite solutions

• none of these

Mathematical Equivalence

ON

Mathematical Equivalence

ON

3x + 10 + 2x = 2 (x + 8)

5x + 10 = 2x + 16

What is the next step? Drag the correct part under the equation. Be sure to put the one labeled left on the left.

d

a

-2x (left side)

/2x (right side)

-2x (right side)

/2x (left side)

Mathematical Equivalence

ON

You rewrote the equation after multiplying the LCD 4 to equal 2x - 20 = 3x + 12 What is the value of x?

Mathematical Equivalence

ON

3x + 10 + 2x = 2 (x + 8)

Label the two steps in the appropriate spots where they took place.

a

b

Combine like terms

Distributive property