Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

When do you flip the inequality symbol?

Back

You flip the inequality symbol when you multiply or divide both sides of the inequality by a negative number.

Front

How do you solve the inequality x + 5 > 7?

Back

Subtract 5 from both sides: x > 2.

Front

What is the solution to the inequality 5w ≥ 30?

Back

w ≥ 6.

Front

What does a closed dot on a number line represent?

Back

A closed dot represents that the number is included in the solution (used for ≤ or ≥).

Front

What does an open dot on a number line represent?

Back

An open dot represents that the number is not included in the solution (used for < or >).

Front

How do you graph the inequality -4x + 14 ≤ 54?

Back

First, solve for x: -4x ≤ 40, then x ≥ -10. Graph with a closed dot at -10.

Front

What is the solution to the inequality -2x < 8?

Back

x > -4 (flip the inequality when dividing by -2).