Solving 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, adding or subtracting, and multiplying or dividing by negative numbers.

Front

How do you solve the inequality 3 < -5n + 2n?

Back

Combine like terms: 3 < -3n. Then divide by -3 (remember to flip the inequality): n < -1.

Front

What does it mean for a value to satisfy an inequality?

Back

A value satisfies an inequality if, when substituted into the inequality, the resulting statement is true.

Front

Does x + 9 > 21 hold true when x = 15?

Back

No, because 15 + 9 = 24, which is greater than 21.

Front

What is the solution to the inequality 6x + 2 < 14?

Back

First, subtract 2 from both sides: 6x < 12. Then divide by 6: x < 2.

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 first step in solving the inequality 2x - 3 > 5?

Back

Add 3 to both sides: 2x > 8.

Front

How do you isolate x in the inequality 4x + 1 ≤ 13?

Back

Subtract 1 from both sides: 4x ≤ 12, then divide by 4: x ≤ 3.

Front

What does the solution x ≥ 2 represent on a number line?

Back

It represents all numbers to the right of 2, including 2 itself.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include the boundary point.