Solving Inequalities Practice

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) to show that one expression is greater than, less than, or equal to another.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you solve the inequality 8x ≥ -32?

Back

Divide both sides by 8: x ≥ -4.

Front

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

Back

The inequality sign flips. For example, if you have -2x ≥ 22 and divide by -2, it becomes x ≤ -11.

Front

Solve the inequality: x + 5 ≤ 13.

Back

Subtract 5 from both sides: x ≤ 8.

Front

Solve the inequality: 8m - 9 > 71.

Back

Add 9 to both sides: 8m > 80. Then divide by 8: m > 10.

Front

Solve the inequality: 7b - 3 < 11.

Back

Add 3 to both sides: 7b < 14. Then divide by 7: b < 2.

Front

What is the first step in solving the inequality -3x + 4 < 10?

Back

Subtract 4 from both sides: -3x < 6.

Front

What does it mean to graph an inequality on a number line?

Back

Graphing an inequality shows all the possible solutions. A closed dot is used for '≤' or '≥', and an open dot is used for '<' or '>'. The line indicates all numbers that satisfy the inequality.