Solving Equations · Two-step equations · 3.2

Two-step: ax − b = c.

Same idea when a number is subtracted: add it back first, then divide. 3x − 4 = 11 → +4 → 3x = 15 → ÷3 → x = 5.

01 / THE IDEA

See it work.

Watch the method

ax − b = c

3x − 4 = 11 → 3x = 15 → x = 5.

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3x−4=113x - 4 = 11
1

The equation

Solve for x — find the value that makes both sides equal.

3x−4=113x - 4 = 11
2

Move the constant

Add 4 to both sides.

3x=153x = 15
3

Divide by the coefficient

Divide both sides by 3 to get x by itself.

x=5x = 5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Solve for x.

Type the value of x — a number or a fraction like 3/2.

streak 0
best 0
…x =
— / WHY IT WORKS

The idea underneath.

Constant first

Undo the −b by adding b to both sides, then undo the coefficient by dividing.

Why it works

Add 4, then divide by 3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 5x + 9 = -6

1

The equation

Solve for x — find the value that makes both sides equal. 5x + 9 = -6

2

Move the constant

Subtract 9 from both sides. 5x = -15

3

Divide by the coefficient

Divide both sides by 5 to get x by itself. x = -3

EX 2medium

Solve 3x - 2 = -5

1

The equation

Solve for x — find the value that makes both sides equal. 3x - 2 = -5

2

Move the constant

Add 2 to both sides. 3x = -3

3

Divide by the coefficient

Divide both sides by 3 to get x by itself. x = -1

EX 3hard

Solve 4x + 6 = 10

1

The equation

Solve for x — find the value that makes both sides equal. 4x + 6 = 10

2

Move the constant

Subtract 6 from both sides. 4x = 4

3

Divide by the coefficient

Divide both sides by 4 to get x by itself. x = 1

04 / COMMON TRAPS

Where students slip.

Trap

Dividing before adding.

Fix

Clear the constant first.

Trap

Subtracting instead of adding.

Fix

To undo −4, add 4.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Solve 4x - 6 = 10

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
C2

Solve 2x - 6 = 12

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
C3

Solve 6x - 1 = 35

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
C4

Solve 2x - 1 = 5

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
Apply

Apply (4)

A1

Solve 2x + 6 = 14

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
A2

Solve 3x - 8 = 16

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
A3

Solve 2x + 7 = 5

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
A4

Solve 2x - 6 = -16

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
Extension

Extension (4)

E1

Solve 3x - 9 = 6

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
E2

Solve 5x + 9 = 34

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
E3

Solve 2x + 9 = 3

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.
E4

Solve 2x + 4 = 8

Need a hint?
  • Add the constant to both sides.
  • Then divide by the coefficient.