Solving Equations · Two-step equations · 3.3

Two-step: x/a + b = c.

With a division and an addition, undo the addition first, then the division. x/2 + 3 = 7 → −3 → x/2 = 4 → ×2 → x = 8.

01 / THE IDEA

See it work.

Watch the method

x/a + b = c

x/2 + 3 = 7 → x/2 = 4 → x = 8.

1 / 3
x/2+3=7x/2 + 3 = 7
1

The equation

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

12x+3=7\frac{1}{2}x + 3 = 7
2

Move the constant

Subtract 3 from both sides.

12x=4\frac{1}{2}x = 4
3

Multiply both sides by 2

x is divided by 2, so multiply both sides by 2 to undo it.

x=8x = 8
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.

Undo in reverse

Clear the constant, then multiply both sides by the divisor.

Why it works

Subtract 3, then multiply by 2.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve x/4 + 5 = 10

1

The equation

Solve for x — find the value that makes both sides equal. 1/4x + 5 = 10

2

Move the constant

Subtract 5 from both sides. 1/4x = 5

3

Multiply both sides by 4

x is divided by 4, so multiply both sides by 4 to undo it. x = 20

EX 2medium

Solve x/2 + 9 = 15

1

The equation

Solve for x — find the value that makes both sides equal. 1/2x + 9 = 15

2

Move the constant

Subtract 9 from both sides. 1/2x = 6

3

Multiply both sides by 2

x is divided by 2, so multiply both sides by 2 to undo it. x = 12

EX 3hard

Solve x/5 + 7 = 15

1

The equation

Solve for x — find the value that makes both sides equal. 1/5x + 7 = 15

2

Move the constant

Subtract 7 from both sides. 1/5x = 8

3

Multiply both sides by 5

x is divided by 5, so multiply both sides by 5 to undo it. x = 40

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying before subtracting.

Fix

Clear the + 3 first.

Trap

Multiplying only the x/2 term.

Fix

Multiply the whole side by the divisor.

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 x/5 + 8 = 15

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
C2

Solve x/4 + 5 = 8

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
C3

Solve x/5 + 3 = 6

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
C4

Solve x/2 + 5 = 11

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
Apply

Apply (4)

A1

Solve x/3 + 4 = 12

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
A2

Solve x/4 + 2 = 7

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
A3

Solve x/2 + 1 = 4

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
A4

Solve x/2 + 5 = 8

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
Extension

Extension (4)

E1

Solve x/4 + 5 = 9

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
E2

Solve x/4 + 8 = 15

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
E3

Solve x/5 + 8 = 13

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.
E4

Solve x/4 + 7 = 13

Need a hint?
  • Subtract the constant first.
  • Then multiply by the divisor.