Introduction to Inequality
An inequality is a mathematical sentence that compares expressions.
It contains the symbols < , > , ≤ or ≥.
To write an inequality, look for the following phrases to determine where
to place the inequality symbol.
Translating Inequalities
Example 1.
Writing an inequality.
Example 2.
Writing an inequality.
a.
𝒙
𝟑
≤
Answer
𝒙
𝟑
b.
5
≤5
𝒙 −𝟒
>
10
Answer
𝒙 − 𝟒 > 𝟏𝟎
c.
Answer
𝟔 + 𝒙 < 𝟐𝟎
𝟔+𝒙
<
20
d. A number more than 12 is more than 8.
A number more than 12
12 + 𝑥
A number less than 12
12 − 𝑥
A number reduced by 12
𝑥 − 12
10 subtracted from a number
𝑥 − 10
Answer: 𝟏𝟐 + 𝒙 > 𝟖
e. The sum of twice a number and 6 is at most 15.
Twice a number
2𝑥
Thrice a number
3𝑥
Sum of a number and 4
𝑥+4
Answer: 𝟐𝒙 + 𝟔 ≤ 𝟏𝟓
On Your Own
Write the word sentence as an inequality.
1) A number x is at most -10.
2) Twice a number y is more than -
5
.
2
3) A number y is no more than -8.
4) A number r multiplied by -4 is at least -
2
.
5
5) A number b minus 4.2 is less than -7.5.
6) A number w added to 2.3 is more than 18.
On Your Own ( Answers )
Write the word sentence as an inequality.
1) A number x is at most -10.
x ≤ - 10
2) Twice a number y is more than -
5
.
2
2y > -
𝟓
𝟐
3) A number y is no more than -8. y < - 8
4) A number r multiplied by -4 is at least 5) A number b minus 4.2 is less than -7.5.
2
.
5
- 4r ≥ -
𝟐
𝟓
b – 4.2 < - 7.5
6) A number w added to 2.3 is more than 18. 2.3 + w > 18