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 -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 ≥ -10 represent on a number line?

Back

It represents all numbers greater than or equal to -10, including -10 itself.

Front

What is the first step in solving the inequality a - 6 ≤ 15 + 8a?

Back

Add 6 to both sides to isolate the variable terms.

Front

What is the solution to the inequality a - 6 ≤ 15 + 8a?

Back

a ≥ -3.

Front

How do you interpret the solution a ≥ -3?

Back

It means that the variable a can take any value greater than or equal to -3.

Front

What is the process to solve the inequality 6 - 2h > 30?

Back

1. Subtract 6 from both sides: -2h > 24. 2. Divide by -2 (flip the inequality): h < -12.

Front

What does the solution h < -12 indicate?

Back

It indicates that h can be any number less than -12.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.

Front

What is an example of a multistep inequality?

Back

Example: 3(x - 2) + 4 < 2x + 10.