2 step inequalities 12/17

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It typically involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 11 > -3y + 2?

Back

First, subtract 2 from both sides: 11 - 2 > -3y, which simplifies to 9 > -3y. Then, divide by -3 (remember to flip the inequality): -3 < y.

Front

What does the inequality -3x ≤ 18 mean?

Back

It means that -3 times x is less than or equal to 18. To solve, divide both sides by -3 (flip the inequality): x ≥ -6.

Front

When do you use an open circle on a graph for an inequality?

Back

An open circle is used when the inequality is > or <, indicating that the endpoint is not included in the solution.

Front

What does a closed circle on a graph indicate?

Back

A closed circle indicates that the number is included in the solution, used for inequalities ≥ or ≤.

Front

Solve the inequality 7n - 1 > 76.

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

What is the solution to the inequality -2x - 3 ≤ 13?

Back

Add 3 to both sides: -2x ≤ 16. Then divide by -2 (flip the inequality): x ≥ -8.

Front

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

Back

The first step is usually to isolate the term with the variable by adding or subtracting a constant from both sides.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips when you multiply or divide both sides of the inequality by a negative number.

Front

How do you graph the solution to the inequality x < 5?

Back

Draw a number line, place an open circle on 5, and shade to the left to indicate all numbers less than 5.