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For example, the algebraic inequalities such as
3x , 7 (The power of the variable x is 1)
and y − 4 . 5 + 2y (The power of the variable y is 1)
are known as linear inequalities in one variable.

Solving a linear inequality in x is to find the values of x that satisfy the inequality.
The process of solving linear inequalities is similar to the process of solving linear
equations. However, we need to consider the direction of the inequality symbol when
solving linear inequalities.

7

Solve each of the following inequalities:
(a) x − 2 < 6 (b) 7x > 28 To solve linear
x inequalities that involve
(c) – , 9 (d) 7 – 4x . 15 multiplication or division,
3
we need to multiply
or divide both sides of
(a) x − 2 < 6 the inequality with an
Add 2 to both sides appropriate number so
x – 2 + 2 < 6 + 2 of the inequality. that the coefficient of the
CHAPTER
7 x < 8 variable becomes 1.

(b) 7x > 28
7x > 28 Divide both sides of the
7 7 inequality by 7.
x > 4 What are the possible
solutions for each of the
x following inequalities if
(c) – , 9 x is an integer?
3
x Multiply both sides of the (a) x > 3
– × (–3) . 9 × (–3) inequality by −3 and reverse (b) x < –5
3 the inequality symbol.
x . –27

(d) 7 – 4x . 15
Subtract 7 from both sides
7 – 4x – 7 . 15 – 7 of the inequality.
– 4x . 8
– 4x , 8 Divide both sides of the Linear inequality in one
– 4 – 4 inequality by −4 and reverse variable has more than
the inequality symbol. one possible solution.
x , –2

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Chapter 7

07 TB Math F1.indd 160 11/10/16 12:16 PM