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 5x - 7 ≥ 8?

Back

Add 7 to both sides to get 5x ≥ 15, then divide by 5 to find x ≥ 3.

Front

What is the first step in solving the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides to simplify the inequality to -4x ≤ 40.

Front

When solving the inequality -3x ≥ 12, what must you remember about the sign?

Back

You must flip the inequality sign when dividing by a negative number, resulting in x ≤ -4.

Front

What does the solution x ≥ -10 represent in the context of the inequality -4x + 14 ≤ 54?

Back

It indicates that x can be any value greater than or equal to -10.

Front

How do you isolate the variable in the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides to get 6t ≤ -6, then divide by 6 to find t ≤ -1.

Front

What is the solution to the inequality 9x - 3 > 6?

Back

Add 3 to both sides to get 9x > 9, then divide by 9 to find x > 1.

Front

What is the significance of flipping the inequality sign?

Back

Flipping the inequality sign is necessary when multiplying or dividing both sides of an inequality by a negative number.

Front

What does the term 'solution set' refer to in inequalities?

Back

The solution set is the range of values that satisfy the inequality.

Front

How can you check if your solution to an inequality is correct?

Back

You can substitute the solution back into the original inequality to see if it holds true.