Inequalities · Year 10
In Inequalities (Year 10) 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?
For example: Does x = −10 satisfy the inequality x + 3 ≤ −3 ?
- Yes
- No
Answer and solution
The answer: Yes
Substitute: −10 + 3 = −7 , so the inequality holds, because −7 ≤ −3 . The answer is yes.
Solving an inequality
For example: Solve the inequality: x − 1 < 13
Answer and solution
The answer: x < 14
Add 1 to both sides: x < 14 . The solution: all the numbers less than 14.
An inequality on the number line
For example: Which picture matches the inequality x ≥ −3 ?
Answer and solution
The answer: Picture A
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
For example: You have £93. Each exercise book costs £14. What is the greatest number of exercise books you can buy?
Answer and solution
The answer: 6
Let x be the number of exercise books. The total cost cannot be more than £93: 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, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).