Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 6x + 2 < 14?

Back

Subtract 2 from both sides: 6x < 12. Then divide by 6: x < 2.

Front

What is the solution to the inequality 28 - k ≥ 7(k - 4)?

Back

First, distribute: 28 - k ≥ 7k - 28. Then combine like terms: 56 ≥ 8k, so k ≤ 7.

Front

How do you solve the inequality -p - 4p > -10?

Back

Combine like terms: -5p > -10. Then divide by -5 (remember to flip the inequality): p < 2.

Front

What does the inequality -4x + 14 ≤ 54 represent?

Back

It represents a range of values for x that satisfy the condition when simplified to x ≥ -10.

Front

What is the first step in solving a multistep inequality?

Back

Identify and isolate the variable by performing inverse operations.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips direction.

Front

What is the solution set for the inequality x + 3 < 5?

Back

x < 2.

Front

How do you check the solution of an inequality?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What is the graphical representation of an inequality?

Back

It is shown on a number line with an open or closed circle indicating whether the endpoint is included.