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, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 2 - 3x ≤ 20?

Back

Subtract 2 from both sides to get -3x ≤ 18, then divide by -3 (remember to flip the inequality sign) to find x ≥ -6.

Front

What does the inequality 22 < 6c + 4 represent?

Back

It represents a relationship where 6c + 4 must be greater than 22. Solving it gives c > 3.

Front

How do you graph the solution to the inequality 77 ≤ 5 + 8n?

Back

First, solve for n to get n ≥ 9. Then, graph a closed circle at 9 and shade to the right.

Front

What is the solution to the inequality 7 - 3n ≥ -53?

Back

To solve, subtract 7 from both sides to get -3n ≥ -60, then divide by -3 to find n ≤ 20.

Front

What is the first step in solving the inequality 7k - 2 ≥ -9?

Back

Add 2 to both sides to isolate the term with k, resulting in 7k ≥ -7.

Front

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 an inequality by a negative number.

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution ensures that the values satisfy the original inequality, confirming that the solution is correct.

Front

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

Back

Graphing an inequality on a number line involves marking the solution set, using open or closed circles to indicate whether endpoints are included.

Front

How do you interpret the solution n ≤ 20?

Back

This means that n can be any number less than or equal to 20.