# Express linear inequalities graphically and algebraically

### Express linear inequalities graphically and algebraically

Linear inequalities can be represented both graphically and algebraically. In this lesson, we will learn how to express linear inequalities as an equation and on a number line.

#### Lessons

• Introduction
i) What is an inequality?
ii) How to solve linear inequalities?
iii) How to graph inequalities on a number line?

• 1.
Express the following inequalities algebraically.
a)

b)

c)

• 2.
Graph each inequality on a number line.
a)
$3.6$ > $x$

b)
$x \le - 3\frac{4}{7}$

c)
$y \le 11$

d)
$5$ < $- \frac{1}{6}$x

• 3.
Find the possible values of $x$ on a number line.
a)
$x \ge 6$ and $x \le 11$

b)
$x$ > $2\frac{3}{7}$ and $x \le 5$

c)
$x \ge - 3.6$ and $x \le 0.25$

d)
$x$ > $-7$ and $x \le - 3\frac{1}{2}$

• 4.
A Christmas tree must be 2 feet or taller so that the farmers will cut it down and sell it in the market.
a)
Use a number line to express the situation.

b)
Express the situation in a statement.