Lesson 8-5: Write and Solve One-Step Addition and Subtraction Inequalities

Property

An inequality is used in algebra to compare two quantities that may have different values. We use four main inequality symbols:
$a < b$ is read $a$ is less than $b$
$a > b$ is read $a$ is greater than $b$
$a \leq b$ is read $a$ is less than or equal to $b$
$a \geq b$ is read $a$ is greater than or equal to $b$

Examples

Property

For any numbers $a$, $b$, and $c$, if $a < b$, then

For any numbers $a$, $b$, and $c$, if $a > b$, then

We can add or subtract the same quantity from both sides of an inequality and still keep the inequality.

Examples

• To solve $x + 7 < 15$, subtract 7 from both sides: $x + 7 - 7 < 15 - 7$, which simplifies to $x < 8$.
• To solve $y - 4 \geq -2$, add 4 to both sides: $y - 4 + 4 \geq -2 + 4$, which simplifies to $y \geq 2$.
• Given $12 > z + 5$, subtract 5 from both sides: $12 - 5 > z + 5 - 5$, so $7 > z$, which means $z < 7$.

Explanation

This property is just like it is for equations. You can add or subtract the same number on both sides of an inequality, and the relationship between the two sides stays the same. The inequality sign does not change.

Property

To solve an inequality using addition or subtraction:

1. We can add the same quantity to both sides of an inequality.
2. We can subtract the same quantity from both sides of an inequality.
3. The direction of the inequality sign remains unchanged when adding or subtracting.

Examples