x 3 x + 3 = 8 Come play with numbers!
Inequalities starters

Can we walk the answer?

# Show it on a number line - Open circle ○ at 3 for `x > 3` or `x < 3` (3 not included) - Closed circle ● at 3 for `x ≥ 3` or `x ≤ 3` (3 included) - Arrow shows which way values go `x > 2` → open circle at 2, arrow to the **right** `x ≤ 5` → closed circle at 5, arrow to the **left** ## Solve like an equation (starter) `x + 2 > 6` Subtract 2: `x > 4` (We will flip the inequality when we multiply/divide by a **negative** later. Not in this first door.) ## How to draw, every time 1. Solve (if needed) until you have `x > a` or `x ≤ a` etc. 2. Mark a on the line. 3. Circle: open if equal is forbidden, closed if allowed. 4. Arrow: right for greater, left for less. 5. Test one number on the arrow and one on the other side. ### Starter solving Inequalities that only add/subtract use the **same** both-sides rule as equations. `x + 2 > 6` `x > 4` We will later flip the inequality when we multiply or divide by a **negative**. That is a new door — not this one. If you meet a negative multiply, stop and ask a teacher or the next course.

By the end of this lesson

Draw x > a and x ≤ a on a number line (open vs closed circle, correct arrow), and solve x + b > c as a starter.

Remember

  • Open circle ○ = the number is not included ( > or < ).
  • Closed circle ● = the number is included ( ≥ or ≤ ).
  • Arrow right = larger numbers. Arrow left = smaller numbers.
  • x > 2 → open at 2, arrow right. x ≤ 5 → closed at 5, arrow left.
  • x + 2 > 6 → subtract 2 → x > 4. (No negative multiply yet.)

Worked examples

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

Example 1 — Draw x > 2

Describe the picture.

  1. Open circle at 2 (2 not allowed)
  2. Arrow to the right (3, 4, 10… allowed)

Answer: ○ at 2, arrow right

Check: 2.1 is allowed; 2 is not.

Example 2 — Draw x ≤ 5

Describe the picture.

  1. Closed circle at 5 (5 allowed)
  2. Arrow to the left

Answer: ● at 5, arrow left

Check: 5, 0, −3 are allowed; 6 is not.

Example 3 — Solve then draw

x + 2 > 6

  1. Subtract 2 both sides: x > 4
  2. Open circle at 4, arrow right

Answer: x > 4

Check: Check a sample: x = 5 → 7 > 6 true. x = 4 → 6 > 6 false.

Common mistakes

Slip Closed circle for x > 2.

Fix Greater-than is open. Equal is not invited.

Line under the symbol → closed.

Slip Arrow left for x > 2.

Fix Greater means to the right.

Numbers increase rightward.

Slip x + 2 > 6 → x > 8 (added 2 instead of subtracting).

Fix Undo +2 by subtracting: x > 4.

Same golden rule as equations.

Try on paper first

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

1. Open or closed circle for x < 0?

Answer: Open at 0

2. Arrow which way for x < 0?

Answer: Left

3. x + 5 ≥ 9 → x …

Answer: ≥ 4

4. Does x > 4 allow 4?

Answer: No

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 road with km markers.

Connect

Indexes and positions in code.

⭐ Star quiz

9 questions

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