Solving Equations · Meet equations · 1.1

Equation vs expression.

An expression is a phrase (2x + 3); an equation says two expressions are EQUAL (2x + 3 = 11). A solution is the value of x that makes the equation true — you can check it by substituting.

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.

x111
=
11111111

Watch the method

Equation vs expression

x = 5 solves x + 3 = 8 because 5 + 3 = 8.

1 / 3
x+3=8x + 3 = 8
1

The equation

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

x+3=8x + 3 = 8
2

Move the constant

Subtract 3 from both sides.

x=5x = 5
3

Read the solution

x is already by itself.

x=5x = 5
— / WHY IT WORKS

The idea underneath.

The equals sign

An equation has an = and asks which value of the variable makes both sides the same. Substitute to check.

Why it works

Put the value back in and see if it balances.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Is x = 9 a solution of x + 8 = 17?

1

Answer

Yes

EX 2medium

Is x = 8 a solution of x + 4 = 11?

1

Answer

No

EX 3hard

Is x = 8 a solution of x + 4 = 11?

1

Answer

No

04 / COMMON TRAPS

Where students slip.

Trap

Treating an expression like an equation.

Fix

No equals sign means nothing to solve — just simplify.

Trap

Not checking the solution.

Fix

Substitute your answer back to be sure.

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

Is x = 1 a solution of x + 3 = 5?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
C2

Is x = 5 a solution of x + 5 = 10?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
C3

Is x = 4 a solution of x + 7 = 11?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
C4

Is x = 3 a solution of x + 3 = 6?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
Apply

Apply (4)

A1

Is x = 3 a solution of x + 8 = 11?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
A2

Is x = 6 a solution of x + 9 = 14?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
A3

Is x = 9 a solution of x + 5 = 14?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
A4

Is x = 6 a solution of x + 2 = 8?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
Extension

Extension (4)

E1

Is x = 9 a solution of x + 3 = 12?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
E2

Is x = 7 a solution of x + 3 = 10?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
E3

Is x = 5 a solution of x + 4 = 9?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.
E4

Is x = 5 a solution of x + 5 = 11?

Need a hint?
  • Substitute the value for x.
  • Check both sides come out equal.