Page 41 - Algebra 1

Inequalities
Inequalities as the name suggests compare two values and tell us whether that the two numbers are less than, equal to or greater than each other.
For example, 4 < 5
You compare two expressions, using an inequality symbol.
The common inequality symbols are: < is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
An algebraic inequality is an inequality comprising of variables. When the value of a variable makes the inequality true, it becomes the solution of the inequality.
Usually, an inequality has more than one solution.
For example,
x ≥ 4 or y < 5
Types of inequalities
❖ Compound inequality
A compound inequality combines two inequalities. We use the word ‘and’ and ‘or’ to describe the compound inequality.
For example,
• x>5andx<–4
This means that x is greater than 5 and less than –4.
• x>–3orx<4
This means that x is greater than –3 or less than 4 or the value of x lies between –3 and 4.
When solving inequalities, the same rule applies as linear equations.
REMEMBER:
• When you add or subtract the same number on each side of the inequality, the inequality remains the same.
If p > q, then p + r > q + r
If p < q, then p – r < q – r
• When multiplying or dividing the same positive number on each side of the inequality, the inequality remains the same.
If p > q, then p × r > q × r, r > 0
If p < q, then p ÷ r < q ÷ r, r >0
• When multiplying or dividing the same negative number on each side of the inequality, the inequality remains the changes.
If p > q, then p × r < q × r, r < 0
If p < q, then p ÷ r > q ÷ r, r < 0
Page 40 of 54
ALGEBRA