x 3 x + 3 = 8 Come play with numbers!
The balance scale

Is equals a button — or a balance?

# What an equation is An **equation** says two things are **equal**. `x + 3 = 10` Left side: `x + 3` Right side: `10` The `=` is a **balance point**, not a button that means “write the answer”. ## Solution A **solution** is the number that makes both sides truly equal. If `x = 7`, then `7 + 3 = 10`. Yes. If `x = 2`, then `2 + 3 = 5`, not 10. No. ## Not the same - Expression: `x + 3` - Equation: `x + 3 = 10` - Inequality: `x + 3 > 10` ## Equation = two pans with the same weight `x + 3 = 10` Left pan: a box and three 1-kg weights. Right pan: a 10-kg weight. They balance. That is all `=` means. A **solution** is the number inside the box that keeps the pans level. Here the box holds 7. ### How to test any suggested answer 1. Cover the letter with the number 2. Work out the left side 3. Work out the right side 4. Ask: same? If yes, it is a solution. If no, it is not. This test never lies. Use it even after you learn fancy solving methods.

By the end of this lesson

Tell an expression from an equation, and test whether a number is a solution by substituting.

Remember

  • An equation says two sides are equal. It needs =.
  • A solution is a number that makes both sides truly equal.
  • To test a guess, replace the letter and compute both sides.
  • x + 3 is an expression. x + 3 = 10 is an equation. x + 3 > 10 is an inequality.
  • = is a balance, not a button that means “write the answer”.

Worked examples

Cover the answer. Try the steps on paper, then open them.

Example 1 — Is 7 a solution of x + 3 = 10?

Substitute and compare.

  1. Left: 7 + 3 = 10
  2. Right: 10
  3. 10 = 10. Yes.

Answer: Yes, x = 7

Check: x = 2 gives 5 = 10, which is false.

Example 2 — Is 4 a solution of 3x = 12?

Substitute x = 4.

  1. Left: 3 × 4 = 12
  2. Right: 12
  3. True.

Answer: Yes

Check: This is the definition of solution — not a feeling.

Example 3 — Sort the three writings

x − 1 / x − 1 = 6 / x − 1 < 6

  1. Expression — a phrase
  2. Equation — a balanced sentence
  3. Inequality — a comparison, not exact equality

Answer: expression ; equation ; inequality

Check: Look only at the middle symbol.

Common mistakes

Slip Thinking the solution of x + 3 = 10 is 10.

Fix The solution is the value of x, which is 7.

10 is the right side, not x.

Slip Calling x + 3 an equation.

Fix No =, so it is an expression.

Phrase vs sentence.

Slip Skipping the check and guessing from the biggest number.

Fix Always substitute.

Guessing is not a method.

Try on paper first

Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.

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

Answer: Yes

5+4=9.

2. Is x = 3 a solution of 2x = 10?

Answer: No

6 ≠ 10.

3. Write an equation that means “a number minus 2 equals 7”.

Answer: x − 2 = 7

4. What symbol must an equation have?

Answer: =

Touch practice

8 tap / type

Tap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.

Optional picture lab

After practice

Real world

A weighing scale at the market.

Connect

Assertions in programs check both sides match.

⭐ Star quiz

9 questions

Finish the touch practice first if you can. Then answer without peeking. Read every “why”.

← Unit Keep the scale balanced →