Key Words for Inequalities Less Than < Greater Than > Is Less Than Is Fewer Than Is Less Than or Equal To Is No More Than Is At Most Greater Than More Than Exceeds Is Greater Than or Equal To Is No Less Than Is At Least Less Than or Equal To ≤ Greater Than or Equal To ≥

Children 10 and under eat free! ≥ ≤ < > X = age of child X ? 10

Must be taller than 40 inches to ride this ride. ≥ ≤ < > X = height X ? 40

≥ ≤ < > X = speed X ? 65

These are called inequalities! X > 40 X ≤ 65 X ≤ 10 These are called inequalities!

Write an inequality for this information. Your age is less than 20 years. (Let x represent your age).

When inequalities have variables (letters) they are open sentences. When you replace the variable with a number, the inequality is either true or false.

Is this inequality true or false? X – 7 < 5 X = 14 14 – 7 < 5 7 < 5 ?

YOU TRY! Is this inequality true or false? 25 + X > 15 X = 10

YOU TRY! Is this inequality true or false? 25 - X ≥ 15 X = 10

Inequalities can be graphed on a number line. “X” represents a number.

There’s a circle involved… < , > ≥ , ≤ With inequalities that do not involve the “equal to” line, the number is NOT included in the graph. This circle is OPEN. With inequalities that do involve the “equal to” line, the number IS included in the graph. The circle is CLOSED.

Let’s graph! x > 4 x < 4 x ≥ 4 Now, write an inequality for the graph below.