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

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

How do you solve the inequality -9x + 7 ≥ 25?

Back

Subtract 7 from both sides: -9x ≥ 18. Then divide by -9 (remember to flip the inequality): x ≤ -2.

Front

What is the solution to the inequality 8m - 9 > 71?

Back

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

Front

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

Back

Subtract 5 from both sides: x > 2.

Front

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

Back

The inequality sign flips.

Front

What is the solution to the inequality x - 4 > 5?

Back

Add 4 to both sides: x > 9.

Front

What is the first step in solving the inequality -2x ≥ 22?

Back

Divide both sides by -2, which flips the inequality sign: x ≤ -11.

Front

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

Back

It means to represent the solution set of the inequality visually, using an open or closed circle and shading.