Solving and Graphing 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 operations like addition, subtraction, multiplication, or division.

Front

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

Back

Subtract 5x from both sides: x + 10 > -12. Then, subtract 10 from both sides: x > -22.

Front

What does the solution x > -22 represent on a number line?

Back

It represents all numbers greater than -22, which is shown as an open circle at -22 and a line extending to the right.

Front

What is the graph of the inequality -2 ≥ n?

Back

The graph shows a closed circle at -2 and a line extending to the left, indicating all numbers less than or equal to -2.

Front

How do you graph the inequality k < 3?

Back

Draw an open circle at 3 and shade to the left, indicating all numbers less than 3.

Front

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

Back

A closed circle indicates that the number is included in the solution (≤ or ≥), while an open circle indicates that the number is not included (< or >).

Front

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

Back

The first step is to isolate the variable by performing inverse operations, similar to solving an equation.

Front

What does the inequality x + 5 < 10 mean?

Back

It means that x must be less than 5, which can be found by subtracting 5 from both sides.

Front

How do you check the solution of an inequality?

Back

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

Front

What is the solution set for the inequality 3x - 4 > 5?

Back

Add 4 to both sides: 3x > 9. Then divide by 3: x > 3.