Finding the values of x that satisfy linear inequalities (solving inequalities)


Solving a linear inequality can be solved in a similar way to solving an equation. However, if you divide or multiply the inequality by a negative number then make sure that you turn the inequality sign around (more than becomes less than and less than become more than).

Example 1

Find the values of x that satisfy the inequality 3x + 2 < 20

First take 2 off both sides of the inequality.

3x < 18

Next divide both sides of the inequality by 3.

x < 6

Example 2

Solve the inequality 5 + x/2 > 31.

First take 5 off both sides of the inequality.

x/2 > 26

Now multiply both sides of the inequality by 2.

x > 52

Example 3

Find the values of x that satisfy the inequality -4x - 3 < 33

First add 3 to both sides of the inequality.

-4x < 36

Next, divide both sides of the inequality by -4. Also make sure that you turn the inequality sign around as you are now dividing by a negative number.

x > -9

Example 4

Find the values of x that satisfy the inequality 10 – x/3 ≥ 8.

First take 10 off both sides of the inequality.

-x/3 ≥-2

Now you need to multiply both sides of the inequality by -3. Again make sure you turn the inequality sign around as you are dividing by a negative number again.

x ≤ 6

Example 5

Solve the inequality 3(2x + 4) > 36

This time multiply the bracket out before you start applying the inverse operations.

6x + 12 > 36

Next take 12 off both sides of the inequality.

6x > 24

Next divide both sides of the inequality by 6. This time, you don’t have to turn the inequality sign around as you are not dividing by a negative number.

x > 4

If you are finding solving these inequalities difficult, then you might need a little more practice on solving linear equations.

Solve equations in math. Solving linear equations.

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Comments 3 comments

Nspeel profile image

Nspeel 5 years ago from Myrtle Beach

BOOKMARKED! Great hub very useful voted up.


carcamping profile image

carcamping 5 years ago

Passing this along to my kids. I can never explain it to them the right way. Thank you for the hub.


lavender3957 5 years ago

wow, I was never good in Math, this is still complicating for me, but in steps, I was able to solve and understand this quite well. Great hub

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