Inequalities — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Add 2 to both sides, then divide by 3.

x < 4

Question 2

(a)List every integer strictly greater than −2 and up to and including 3.

n = −1, 0, 1, 2, 3

Question 3

(a)Subtract 5, then divide by 2.

x > −2

Question 4

(a)List every integer from −3 up to but not including 2.

−3, −2, −1, 0, 1

Question 5

(a)Subtract 4 from both sides, then multiply by −1 (reversing the inequality).

x ≥ −6

Question 6

(a)Collect x terms on one side.

x < 5

Question 7

(a)A closed (filled) circle at −2, with an arrow extending to the right.

Filled circle at −2, shaded/arrow to the right

Question 8

(a)Divide both sides by −2, remembering to reverse the inequality sign.

x < −4

Question 9

(a)Subtract 5, then divide by −2 (reversing the inequality).

x ≤ 4

Question 10

(a)Subtract 3 from all three parts, then divide by 2.

2 < x ≤ 6

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