Linear Inequalities (One Variable)

Linear Inequalities (One Variable)

How to solve linear inequalities (one variable) problems: examples and their solutions.

Example 1

Solve the given inequality. 7x + 5 ≥ 19

Solve the linear inequality
like solving a linear equation:

Move the constant term +5 to the right side.

Moving the terms on both side (= adding, subtracting)
doesn't change the order of the inequality sign.

Then divide both sides
by the x term's coefficient: 7.

The divisor 7 is (+).

So the order of the inequality sign
doesn't change.

Example 2

Solve the given inequality. 2 - 3a < 8

Move the constant term 2 to the right side.

Then divide both sides
by the a term's coefficient: -3.

The divisor -3 is (-).

So the order of the inequality sign
does change.

So keep this in mind:
Multiplying and dividing (-), a negative number,
does change the order of the inequality sign.