Solving Equations · Meet equations · 1.3

Inverse operations.

Every operation has an inverse that undoes it: + and −, × and ÷. To get x by itself, apply the inverse. For 3x = 12, x is multiplied by 3, so divide both sides by 3: x = 4.

01 / THE IDEA

See it work.

Keep it balanced

Whatever you do to one side, do to the other.

An x-box weighs the unknown; a 1-circle weighs one.

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Watch the method

Inverse operations

3x = 12 → divide both sides by 3 → x = 4.

1 / 2
3x=123x = 12
1

The equation

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

3x=123x = 12
2

Divide by the coefficient

Divide both sides by 3 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.

streak 0
best 0
…x =
— / WHY IT WORKS

The idea underneath.

Opposites undo

Subtraction undoes addition; division undoes multiplication. Apply the inverse to isolate x.

Why it works

×3 is undone by ÷3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 3x = 15

1

The equation

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

2

Divide by the coefficient

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

EX 2medium

Solve 3x = 12

1

The equation

Solve for x — find the value that makes both sides equal. 3x = 12

2

Divide by the coefficient

Divide both sides by 3 to get x by itself. x = 4

EX 3hard

Solve 2x = 14

1

The equation

Solve for x — find the value that makes both sides equal. 2x = 14

2

Divide by the coefficient

Divide both sides by 2 to get x by itself. x = 7

04 / COMMON TRAPS

Where students slip.

Trap

Using the same operation instead of the inverse.

Fix

To undo ×3, divide — don’t multiply.

Trap

Forgetting to apply it to both sides.

Fix

Inverse both sides equally.

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 5x = 15

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
C2

Solve 2x = 8

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
C3

Solve 6x = 30

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
C4

Solve 4x = 20

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
Apply

Apply (4)

A1

Solve 3x = 15

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
A2

Solve 2x = 4

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
A3

Solve 4x = 24

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
A4

Solve 4x = 28

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
Extension

Extension (4)

E1

Solve 2x = 16

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
E2

Solve 6x = 48

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
E3

Solve 5x = 10

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.
E4

Solve 5x = 10

Need a hint?
  • Find what’s done to x.
  • Apply the inverse to both sides.