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 graph the inequality -2 ≥ n?

Back

You would graph a solid dot at -2 and shade to the left, indicating all values less than or equal to -2.

Front

What is the first step to solve the inequality 3(x - 2) < 2(x + 9)?

Back

Distribute both sides: 3x - 6 < 2x + 18.

Front

What is the solution to the inequality 3(x - 2) < 2(x + 9)?

Back

x < 24.

Front

How do you write an inequality for cell plan A being greater than cell plan B?

Back

40 + 0.04x > 30 + 0.09x.

Front

What does the inequality k < 3 represent on a number line?

Back

All values to the left of 3, not including 3 itself.

Front

If you want to spend at most $1200 on a laptop after a $400 down payment, what inequality represents your monthly payments?

Back

12x + 400 < 1200.

Front

What is the process of solving a multi-step inequality?

Back

1. Simplify both sides if necessary. 2. Isolate the variable by performing inverse operations. 3. Graph the solution.

Front

What does it mean if an inequality has a solid dot on a number line?

Back

It indicates that the number is included in the solution set (≤ or ≥).

Front

What does it mean if an inequality has an open dot on a number line?

Back

It indicates that the number is not included in the solution set (< or >).