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: 3 < -5n + 2n?

Back

Combine like terms to get 3 < -3n, then divide by -3 (remember to flip the inequality) to find n < -1.

Front

What does the inequality symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to another value.

Front

How do you graph the inequality 4(b+3) - 6 ≤ -2?

Back

First, solve for b: 4(b+3) ≤ 4. Then, graph the line b = -1, shading to the left to indicate all values less than or equal to -1.

Front

What is the first step in solving the inequality x - 14 < -8?

Back

Add 14 to both sides to isolate x, resulting in x < 6.

Front

What does the solution m ≥ -5 represent on a number line?

Back

It represents all numbers greater than or equal to -5, including -5 itself, shaded to the right on the number line.

Front

How do you solve the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides to get x + 10 > -12, then subtract 10 to find x > -22.

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 does the term 'solution set' refer to in inequalities?

Back

The solution set is the set of all values that satisfy the inequality.

Front

How can you check if your solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it holds true.