Two Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. For example, in the inequality 2x + 3 > 7, you would first subtract 3 from both sides and then divide by 2.

Front

How do you solve the inequality 16 - 4a > 8?

Back

Subtract 16 from both sides: -4a > -8. Then divide by -4 (remember to flip the inequality sign): a < 2.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value can be either less than or exactly equal to another value.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value can be either greater than or exactly equal to another value.

Front

How do you graph the inequality x ≤ 3?

Back

To graph x ≤ 3, draw a number line, place a closed dot on 3 (indicating that 3 is included), and shade to the left to show all numbers less than or equal to 3.

Front

What is the solution to the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10. Then divide by 2: k ≤ -5.

Front

When do you use an open dot on a graph of an inequality?

Back

An open dot is used when the inequality symbol is '<' or '>', indicating that the endpoint is not included in the solution.

Front

Solve the inequality -3w - 2 < -17.

Back

Add 2 to both sides: -3w < -15. Then divide by -3 (flip the inequality sign): w > 5.

Front

What is the first step to solve the inequality 77 ≤ 5 + 8n?

Back

Subtract 5 from both sides: 72 ≤ 8n.

Front

What is the final solution for the inequality 77 ≤ 5 + 8n?

Back

Divide by 8: n ≥ 9.