Plugging in and Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (e.g., <, >, ≤, ≥) to show that one expression is not equal to the other.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' 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

The symbol '≤' 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 7k - 2 ≥ -9?

Back

Add 2 to both sides: 7k ≥ -7. Then divide by 7: k ≥ -1.

Front

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

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the solutions of the inequality on a number line, using open or closed dots to indicate whether endpoints are included.

Front

When do you use an open dot on a graph?

Back

An open dot is used when graphing inequalities with < or >, indicating that the endpoint is not included in the solution.

Front

When do you use a closed dot on a graph?

Back

A closed dot is used when graphing inequalities with ≤ or ≥, indicating that the endpoint is included in the solution.

Front

Solve the inequality 8x ≥ -32.

Back

Divide both sides by 8: x ≥ -4.

Front

What is the solution to the inequality x + 5 < 12?

Back

Subtract 5 from both sides: x < 7.