Linear Inequality (One Variable)

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

Example 1

Example

Solution

Solve the inequality just like solving an equation.
First move +5 to the right side.
Then the left side is 7x.
And the right side is 19, change the sign of +5, -5.

19 - 5 = 14
So 7x ≥ 14.

To remove the coefficient 7,
divide both sides by 7.
When multiplying or dividing a minus number on both sides, the order of the inequality sign changes.
In this case, 7 is not a minus number.
So the order of the inequality sign doesn't change.
Then the left side is x.
The order of the inequality sign doesn't change.
And the right side is 14/7.

14/7 = 2
So x ≥ 2.

x ≥ 2
This is the answer.

Example 2

Example

Solution

First move 2 to the right side.
Then the left side is -3x.
And the right side is 8, change the sign of 2, -2.

8 - 2 = 6
So -3x < 6.

To remove the coefficient -3,
divide both sides by -3.
When multiplying or dividing a minus number on both sides, the order of the inequality sign changes.
In this case, -3 is a minus number.
So the order of the inequality sign does change.
Then the left side is x.
The order of the inequality sign does change: < → >.
And the right side is 6/(-3).

6/(-3) = -2
So x > -2.

x > -2
This is the answer.