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 -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 x ≥ -10 represent in a graph?

Back

It represents all values of x that are greater than or equal to -10, including -10 itself, extending to the right on a number line.

Front

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

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the first step in solving a multistep inequality?

Back

The first step is to simplify both sides of the inequality, which may involve distributing, combining like terms, or moving constants.

Front

What does the inequality a - 6 ≤ 15 + 8a mean?

Back

It means that the value of a, when decreased by 6, is less than or equal to the value of 15 plus 8 times a.

Front

How do you isolate the variable in the inequality a - 6 ≤ 15 + 8a?

Back

Add 6 to both sides: a ≤ 21 + 8a. Then, subtract 8a from both sides: -7a ≤ 21. Finally, divide by -7 (flip the inequality): a ≥ -3.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

Distribute: -2x - 4 < 14. Add 4 to both sides: -2x < 18. Divide by -2 (flip the inequality): x > -9.

Front

What does the solution x < 1 indicate?

Back

It indicates that x can take any value less than 1, not including 1 itself.

Front

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

Back

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