Solving Equations · Meet equations · 1.2

The balance rule.

An equation is a balance. To keep it balanced, whatever you do to one side you must do to the other. To solve x + 4 = 9, subtract 4 from both sides: x = 5.

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.

x1111
=
111111111

Watch the method

The balance rule

x + 4 = 9 → subtract 4 from both sides → x = 5.

1 / 3
x+4=9x + 4 = 9
1

The equation

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

x+4=9x + 4 = 9
2

Move the constant

Subtract 4 from both sides.

x=5x = 5
3

Read the solution

x is already 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.

Stay balanced

Adding, subtracting, multiplying, or dividing both sides by the same amount keeps the equation true.

Why it works

A scale stays level if you change both pans equally.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve x + 8 = 19

1

The equation

Solve for x — find the value that makes both sides equal. x + 8 = 19

2

Move the constant

Subtract 8 from both sides. x = 11

3

Read the solution

x is already by itself. x = 11

EX 2medium

Solve x + 1 = 7

1

The equation

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

2

Move the constant

Subtract 1 from both sides. x = 6

3

Read the solution

x is already by itself. x = 6

EX 3hard

Solve x + 3 = 11

1

The equation

Solve for x — find the value that makes both sides equal. x + 3 = 11

2

Move the constant

Subtract 3 from both sides. x = 8

3

Read the solution

x is already by itself. x = 8

04 / COMMON TRAPS

Where students slip.

Trap

Changing only one side.

Fix

Whatever you do, do it to BOTH sides.

Trap

Adding when you should subtract.

Fix

Use the inverse operation to undo.

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 + 8 = 19

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
C2

Solve x + 9 = 18

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
C3

Solve x + 8 = 20

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
C4

Solve x + 2 = 12

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
Apply

Apply (4)

A1

Solve x + 8 = 14

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
A2

Solve x + 7 = 12

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
A3

Solve x + 3 = 5

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
A4

Solve x + 3 = 6

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
Extension

Extension (4)

E1

Solve x + 5 = 16

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
E2

Solve x + 9 = 17

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
E3

Solve x + 8 = 15

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.
E4

Solve x + 5 = 16

Need a hint?
  • Do the same thing to both sides.
  • Use the inverse operation.