# Inequalities · Grade 8

> Inequalities, Grade 8: Does the number satisfy the inequality? and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Inequalities (Grade 8) you practise 4 skills: Does the number satisfy the inequality? · Solving an inequality · An inequality on the number line · Word problems with inequalities.

In an inequality the two sides do not have to be equal: one of them is less than or greater than the other. There are four signs: less than, greater than, less than or equal to, and greater than or equal to.

An inequality usually has infinitely many solutions, so they are shown on the number line: an open circle when the number itself is not a solution, a filled circle when it is, and a ray towards all the other solutions.

Solve an inequality like an equation: add, subtract, multiply or divide both sides by the same number.

When you multiply or divide by a negative number, reverse the sign: less than becomes greater than, and greater than becomes less than.

**Tip:** At the end, check: choose one number from the solution, put it into the original inequality and make sure it holds.

## What you learn

### Does the number satisfy the inequality?

- Example: Does x = −10 satisfy the inequality x + 3 ≤ −3 ?
- Options: Yes · No
- Answer: Yes
- Solution: Substitute: −10 + 3 = −7 , so the inequality holds, because −7 ≤ −3 . The answer is yes.

### Solving an inequality

- Example: Solve the inequality: x − 1 < 13
- Answer: x < 14
- Solution: Add 1 to both sides: x < 14 . The solution: all the numbers less than 14.

### An inequality on the number line

- Example: Which picture matches the inequality x ≥ −3 ?
- Options: Picture A (Picture A: a number line with a filled circle at −3 and a ray to the right.) · Picture B (Picture B: a number line with a filled circle at −3 and a ray to the left.) · Picture C (Picture C: a number line with an open circle at −3 and a ray to the right.) · Picture D (Picture D: a number line with an open circle at −3 and a ray to the left.)
- Answer: Picture A
- Solution: The sign includes equality, so the circle is filled. The solutions are the numbers greater than or equal to −3, so the ray goes to the right. The answer is Picture A.

### Word problems with inequalities

- Example: You have 93 shekels. Each exercise book costs 14 shekels. What is the greatest number of exercise books you can buy?
- Answer: 6
- Solution: Let x be the number of exercise books. The total cost cannot be more than 93 shekels: 14x ≤ 93 Check the whole numbers next to the boundary: 14 × 6 = 84 ≤ 93 14 × 7 = 98 > 93 So you can buy at most 6 exercise books.

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education's grade 8 transition maths curriculum (2026–27).

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