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, adding or subtracting, and multiplying or dividing by a number.

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 a closed dot represent when graphing inequalities?

Back

A closed dot indicates that the number is included in the solution set, used with ≤ and ≥.

Front

What does an open dot represent when graphing inequalities?

Back

An open dot indicates that the number is not included in the solution set, used with < and >.

Front

How do you graph the inequality 6 > x?

Back

You would place an open dot at 6 and shade to the left, indicating all numbers less than 6.

Front

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

Back

a < -2.

Front

What is the first step in solving the inequality 3x - 5 > 4?

Back

Add 5 to both sides: 3x > 9.

Front

What do you do when you multiply or divide both sides of an inequality by a negative number?

Back

You must flip the inequality sign.

Front

What is the solution to the inequality 2x + 3 ≤ 11?

Back

x ≤ 4.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ includes the number, while < does not.