Solving Multi-Step Inequalities

Front

What is a multi-step inequality?

Back

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

x ≥ -10.

Front

What does the inequality 12x + 400 < 1200 represent in a real-world context?

Back

It represents the maximum monthly payment you can afford for a laptop after a down payment.

Front

How do you write an inequality for when Cell plan A is greater than Cell plan B?

Back

40 + 0.04x > 30 + 0.09x.

Front

What is the solution to the inequality 12 ≥ 15 - 6y?

Back

y ≥ ½.

Front

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

Back

Open circle.

Front

What is the difference between an open circle and a closed circle on a number line?

Back

An open circle indicates that the number is not included in the solution (e.g., <), while a closed circle indicates that the number is included (e.g., ≤).

Front

What is the first step in solving a multi-step inequality?

Back

Isolate the variable by performing inverse operations.

Front

What does it mean to check your solution set in an inequality?

Back

It means substituting values back into the original inequality to verify that they satisfy the inequality.

Front

How do you graph the solution to the inequality x ≥ 3?

Back

Draw a closed circle on 3 and shade to the right.