8th Grade - Multi-Step Multi-variable Equations

Overview

• You have already learned how to solve simple equations like $x-2=5$. These can be solved in one step.
• The equations like $7x-3=18$ or $2x+3=3x-3$ would need more than one step to solve.

Solving Two Step Equations

• The two-step equations can be solved using inverse operations.

Solving Multi Step Multi Variable Equations

• If there is a parenthesis, use the distributive property to get rid of it.
• Combine all like terms after using the distributive property.
• Use inverse operations to isolate the variables, if needed.
• Finally, eliminate the constant or variable term from one side of the equation.

Solved Examples

• Solve $2x-10=30$

Add 10 to both sides (addition property of equality).

$2x-10+10=30+10$

$2x=40$

Divide both sides by 2 (division property of equality).

$\frac{2x}{2}=\frac{40}{2}$

$x=20$

• Solve $4\left(x+2\right)=20$

Use the distributive property.

$4x+8=20$

Subtract 8 from both sides (subtraction property of equality).

$4x+8-8=20-8$

$4x=12$

Divide both sides by 4 (division property of equality).

$\frac{4x}{4}=\frac{12}{4}$

$x=3$

Cheat Sheet

• Get rid of the parenthesis first, if any.
• If you have to perform any operation like adding a term, subtracting a term, multiplying, or dividing, perform the same operation on the other side.

Blunder Area

• Whatever you do to one side of the equation, do the same to the other side of the question.
• Pay close attention to the signs while using the distributive property.
• Pay close attention to the signs while doing inverse operations.