Solving MultiStep Inequalities

Front

What is a multi-step inequality?

Back

A multi-step 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 9 ≥ -2m + 2 − 3?

Back

First, simplify: 9 ≥ -2m - 1. Then, add 1 to both sides: 10 ≥ -2m. Finally, divide by -2 (remember to flip the inequality): m ≥ -5.

Front

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

Back

The symbol '>' means 'greater than' and indicates that the value on the left is larger than the value on the right.

Front

When graphing an inequality, what does an open dot represent?

Back

An open dot represents that the endpoint is not included in the solution set, used for inequalities with '<' or '>'.

Front

What is the solution to the inequality -3 − 6(4x + 6) > -111?

Back

First, simplify: -3 - 24x - 36 > -111. Combine like terms: -24x > -72. Divide by -24 (flip the inequality): x < 3.

Front

How do you represent the inequality for spending at most $1200 on a laptop with a $400 down payment?

Back

The inequality is 12x + 400 < 1200, where x is the monthly payment.

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

How do you solve the inequality 3x - 5 > 4?

Back

Add 5 to both sides: 3x > 9. Then, divide by 3: x > 3.

Front

What is the first step in solving the inequality 2(x + 3) < 10?

Back

Distribute the 2: 2x + 6 < 10.