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 operations such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality -8(m + 2) < 4(5 + 2m)?

Back

First, distribute: -8m - 16 < 20 + 8m. Then, combine like terms: -16 < 20 + 16m. Finally, isolate m: m < -2.

Front

What does the solution m = -2 indicate in the context of the inequality -8(m + 2) < 4(5 + 2m)?

Back

It indicates that -2 is a value that satisfies the inequality, meaning when m is -2, the inequality holds true.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

x ≥ -10.

Front

How do you isolate x in the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (remember to flip the inequality sign) to find x ≥ -10.

Front

What does the inequality 18 ≥ 5k + 4k represent?

Back

It represents a relationship between the variable k and the constant 18, where the sum of 5k and 4k must be less than or equal to 18.

Front

What is the solution to the inequality 18 ≥ 5k + 4k?

Back

k ≤ 2.

Front

How do you combine like terms in the inequality 18 ≥ 5k + 4k?

Back

Add 5k and 4k to get 18 ≥ 9k, then divide both sides by 9 to find k ≤ 2.

Front

What is the significance of the inequality sign in multistep inequalities?

Back

The inequality sign indicates the relationship between two expressions, showing whether one is greater than, less than, or equal to the other.

Front

What is a common mistake when solving multistep inequalities?

Back

A common mistake is forgetting to flip the inequality sign when multiplying or dividing by a negative number.