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Solving Equations

Learn how to isolate variables step-by-step and solve any basic equation with confidence.

+
•X =

X

 
 

What You'll Learn:

  • Solve one-step equations
  • Check your answers
  • Avoid common mistakes
  • Solve multi-step equations

Lesson 1:

One-Step Equations

Undo the operations to isolate the variables

  • x + 5 = 12
  • ⟶
  • x = 12 - 5
  • ⟶
  • x = 7

Lesson 2:

Two-Step Equations

Variable on both sides

2x + 3 = 11
2x = 8
⟶
2x + 3 – 3 = 11 – 3
2x = 8
⟶
2x = 8
↙
x = 4
2x + 3 = 11
⟶
2x + 3 − 3 = 11 − 3
2x 2 = 8 2
⟶
2x = 8
x = 4
Check: plug x = 4 back in:
1. 2x + 3 = 11 ⟶ 2(4) + 3 = 11 ⟶ 8 + 3 = 11 ✓

Lesson 3:

Variables on Both Sides

Isolate the variable by undoing operations in reverse.

5x + 2 = 3x + 8
⟶
2x + 2 = 8
⟶
2x = 6
⟶
x = 3 ✓

Practice Problems

Easy

  • x + 4 = 10

Medium

  • 2x + 5 = 15

Challenge

  • 4x − 3 = 2x + 9

Common Mistakes to Avoid

  • Forgetting to do the same thing to both sides
  • Distributing incorrectly
  • Making arithmetic errors

Quick Recap:

To solve equations: isolate the variable
by undoing the operations in reverse order.

±
—
+
÷
—

=

ISOLATE

=

O

  • Undo addition or subtraction to isolate the variable.
  • Undo multiplication or division.
  • Check your solution.
Answer Key:
Easy: x = 6
Medium: x = 5
Challenge: x = 6

Next:

Graphing & Slope
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