Express linear inequalities graphically and algebraically - Inequalities

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.

Basic Concepts
Cartesian plane
Comparing and ordering rational numbers

Related Concepts
Graphing linear inequalities in two variables
Graphing systems of linear inequalities
Graphing quadratic inequalities in two variables
Graphing systems of quadratic inequalities

Lessons

1.
Express the following inequalities algebraically.
2.
Graph each inequality on a number line.
3.
Find the possible values of $x$ on a number line.
4.
A Christmas tree must be 2 feet or taller so that the farmers will cut it down and sell it in the market.

Express linear inequalities graphically and algebraically

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GeometryCartesian plane

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Intro Lesson

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Lesson: 1a

Lesson: 1b

Lesson: 1c

Lesson: 2a

Lesson: 2b

Lesson: 2c

Lesson: 2d

Lesson: 3a

Lesson: 3b

Lesson: 3c

Lesson: 3d

Lesson: 4a

Lesson: 4b

Intro

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Lessons

Intro Lesson

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)

3.63.6 3.6 > x xx

b)

x≤−347x \le - 3\frac{4}{7}x≤−374​

c)

y≤11y \le 11y≤11

d)

55 5 < −16 - \frac{1}{6}−61​x

3.

Find the possible values of xxx on a number line.

a)

x≥6x \ge 6x≥6 and x≤11x \le 11x≤11

b)

xx x > 237 2\frac{3}{7}273​ and x≤5x \le 5x≤5

c)

x≥−3.6x \ge - 3.6x≥−3.6 and x≤0.25x \le 0.25x≤0.25

d)

xx x > −7 -7−7 and x≤−312x \le - 3\frac{1}{2}x≤−321​

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.

Express linear inequalities graphically and algebraically

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Geometry
Cartesian plane

Basic Math
Comparing and ordering rational numbers

or

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

$3.6$ > $x$

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

$y \le 11$

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

Find the possible values of $x$ on a number line.

$x \ge 6$ and $x \le 11$

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

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

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