# Linear Inequality (One Variable)

How to solve a linear inequality (one variable): 2 examples and their solutions.

## Example7x + 15 ≥ 19

Solution

Solution (Detail)

Solve the linear inequality

just like solving an equation.

Move +5 to the right side.

Then 7x ≥ 14.

Divide both sides by 7.

7 is [+].

Then the order of the inequality sign

[doesn't change].

So x ≥ 2.

When multiplying or dividing [+] on both sides,

the order of the inequality sign [doesn't change].

So

x ≥ 2

is the answer.

## Example2 - 3x < 8

Solution

Solution (Detail)

Solve the linear inequality

just like solving an equation.

Move 2 to the right side.

Then -3x < 6.

Divide both sides by -3.

-3 is [-].

Then the order of the inequality sign

[does change].

So x > -2.

When multiplying or dividing [-] on both sides,

the order of the inequality sign [does change].

6/(-3) = -2

Divide Negative Numbers

So

x > -2

is the answer.