Solving Equations · Two-step equations · 3.1

Two-step: ax + b = c.

A two-step equation needs two inverse operations, in reverse order: first undo the addition/subtraction, then undo the multiplication. 2x + 3 = 11 → −3 → 2x = 8 → ÷2 → x = 4.

01 / THE IDEA

See it work.

Watch the method

Two steps: ax + b = c

2x + 3 = 11 → 2x = 8 → x = 4.

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2x+3=112x + 3 = 11
1

The equation

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

2x+3=112x + 3 = 11
2

Move the constant

Subtract 3 from both sides.

2x=82x = 8
3

Divide by the coefficient

Divide both sides by 2 to get x by itself.

x=4x = 4
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.

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…x =
— / WHY IT WORKS

The idea underneath.

Reverse order

Peel operations off in the opposite order they were applied: constants first, then the coefficient.

Why it works

Take off the +3, then the ×2.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 2x + 7 = -3

1

The equation

Solve for x — find the value that makes both sides equal. 2x + 7 = -3

2

Move the constant

Subtract 7 from both sides. 2x = -10

3

Divide by the coefficient

Divide both sides by 2 to get x by itself. x = -5

EX 2medium

Solve 5x + 9 = 19

1

The equation

Solve for x — find the value that makes both sides equal. 5x + 9 = 19

2

Move the constant

Subtract 9 from both sides. 5x = 10

3

Divide by the coefficient

Divide both sides by 5 to get x by itself. x = 2

EX 3hard

Solve 2x + 3 = 15

1

The equation

Solve for x — find the value that makes both sides equal. 2x + 3 = 15

2

Move the constant

Subtract 3 from both sides. 2x = 12

3

Divide by the coefficient

Divide both sides by 2 to get x by itself. x = 6

04 / COMMON TRAPS

Where students slip.

Trap

Dividing before subtracting.

Fix

Undo the + or − first, then the × or ÷.

Trap

Dividing only one term.

Fix

Divide the WHOLE side by the coefficient.

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 = 18

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
C2

Solve 2x + 5 = 17

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
C3

Solve 2x - 3 = 5

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
C4

Solve 4x - 9 = 3

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
Apply

Apply (4)

A1

Solve 2x + 5 = 7

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
A2

Solve 2x + 2 = 4

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
A3

Solve 5x + 3 = -2

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
A4

Solve 2x + 1 = 11

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
Extension

Extension (4)

E1

Solve 6x - 9 = 33

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
E2

Solve 6x + 9 = 63

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
E3

Solve 5x - 2 = -22

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.
E4

Solve 4x - 7 = 21

Need a hint?
  • Subtract the constant first.
  • Then divide by the coefficient.