Solving Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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 -7x + 15 ≥ -20?

Back

First, subtract 15 from both sides: -7x ≥ -35. Then, divide by -7 (remember to flip the inequality sign): x ≤ 5.

Front

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

Back

The inequality sign flips when you multiply or divide both sides of the inequality by a negative number.

Front

What is the solution to the inequality -2x ≥ 22?

Back

Divide both sides by -2 (flip the sign): x ≤ -11.

Front

What does a closed circle on a number line represent?

Back

A closed circle represents that the number is included in the solution set (used with ≤ or ≥).

Front

What does an open circle on a number line represent?

Back

An open circle represents that the number is not included in the solution set (used with < or >).

Front

How do you graph the inequality a ≥ 11?

Back

Draw a closed circle at 11 and shade to the right to indicate all numbers greater than or equal to 11.

Front

What is the solution to the inequality -7 + 10z > -27?

Back

Add 7 to both sides: 10z > -20. Then divide by 10: z > -2.