Solving Multi-Step 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 -4x + 14 ≤ 54?

Back

1. Subtract 14 from both sides: -4x ≤ 40. 2. Divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What does the solution x ≤ 24 represent?

Back

It means that x can be any number less than or equal to 24.

Front

What does the inequality s ≤ 18 indicate?

Back

It indicates that the number of students, s, can be 18 or fewer.

Front

When graphing the inequality b < 6, what type of circle is used?

Back

An open circle is used to indicate that 6 is not included in the solution.

Front

What is the first step in solving the inequality 12 ≥ 15 - 6y?

Back

The first step is to isolate the term with the variable by subtracting 15 from both sides: -3 ≥ -6y.

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 solution to the inequality 3x - 5 > 4?

Back

1. Add 5 to both sides: 3x > 9. 2. Divide by 3: x > 3.

Front

How do you check the solution of an inequality?

Back

Substitute a value from the solution set back into the original inequality to see if it holds true.

Front

What does the inequality y ≥ ½ mean in terms of y's possible values?

Back

It means that y can be any number greater than or equal to ½.