Inequalities and Linear Programming

155.
(a) It is given that:
72 ≤ q ≤ 88 14 ≤ r ≤ 30  and 100 ≤ m ≤ 150 .
Find the maximum possible value of r m-q , leaving your answer as a fraction in its simplest form.
................................. [3]
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156.
The inequality 16<9-5x<24 has solution a<x<b .
Find the values of a and b.
a = ......................... [2]b = ......................... [2]
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157.
Solve: 14n>11n+6
n ......................... [2]
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158.
On the number line below, show the set of values of x for which -2<x≤4 .
x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
See diagram [3]
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159.
(a) n is an integer. -1≤n<4 .
List the possible values of n.
(b) Write down the inequality shown in the diagram.
x -5 -4 -3 -2 -1 0 1 2 3 4 5

(c) Solve: y-2>5
(a) ......................... (b) ......................... (c) .........................
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160.
Solve the inequality: 3p-7>11
.................................
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161.
(a) Show the inequality x<3 on the number line below.
Empty number line x -4 -3 -2 -1 0 1 2 3 4 5

(b) Solve the inequality: 4x-7≥13
(a) See diagram (b) .........................
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