Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is larger or smaller than the other.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

x ≥ -10

Front

What is the solution to the inequality 5z - 2 - 2z < 13?

Back

z < 5

Front

What does the inequality 10 ≥ x - 3 represent?

Back

It represents that x can be any value less than or equal to 13.

Front

When solving inequalities, what happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips (changes direction).

Front

What is the solution to the inequality 7(x + 3) < 5x + 13?

Back

x < -4

Front

What does the symbol '≤' mean?

Back

It means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

It means 'greater than or equal to'.

Front

How do you graph the solution of an inequality on a number line?

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.