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

1. Distribute: -8m - 16 < 20 + 8m 2. Combine like terms: -16 < 20 + 16m 3. Isolate m: -36 < 16m 4. Divide by 16: m > -2.

Front

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

Back

It means that -2 is a value that satisfies the inequality, making the left side less than the right side.

Front

What is the first step in solving the inequality 18 ≥ 5k + 4k?

Back

Combine like terms: 18 ≥ 9k.

Front

What is the solution to the inequality 18 ≥ 9k?

Back

k ≤ 2.

Front

What does the symbol '≥' mean in an inequality?

Back

It means 'greater than or equal to'.

Front

How do you interpret the solution k ≤ 2?

Back

It means that k can be any number less than or equal to 2.

Front

What is the process for solving the inequality 6x + 2 < 14?

Back

1. Subtract 2 from both sides: 6x < 12. 2. Divide by 6: x < 2.

Front

What does the solution x < 2 indicate?

Back

It indicates that x can take any value less than 2.

Front

What is the importance of checking your solution in an inequality?

Back

Checking ensures that the solution satisfies the original inequality and helps avoid mistakes.