Equations with Variables on Both Sides and Special Solutions

When solving an equation with variables on BOTH sides, we must first move all variables to the LEFT side of the equation.

• True

• False

Solve:
7x = 3x + 24

• 6

• 10

• 14

• 4

Solve for x:
4(1-x) + 3x = -2(x+1)

• x = -6

• x = 6

• x = 3

Solve:
2(4x-3) - 8 = 4 + 2x

• x = 5/3

• x = 3

• x = 1

• x = 2

Solve:
5y + 34 = -2(-7y+1)

• y = -4

• y = 9

• y = 4

• y = 36/19

Solve the equation:
-8x - 8 + 3(x-2) = -3x + 2

• x = -8

• x = 8

• x = 2

• x = -2

What is the first step you should take to solve this problem?

• subtract 8n to both sides

• multiply 6n to both sides

• combine the like terms 4n + -6n

• add 1 to both sides

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

What is the error?

• Adding 2x to 3x

• Subtracting 5 from both sides

• Adding 2x to -2x

• Dividing by 5 on both sides

Where is the first mistake?

• Subtracting 3 on both sides

• Distributing the 9

• Subtracting 9x on both sides

• Inequality error