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 such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality 6(n + 2) < -72?

Back

First, distribute the 6: 6n + 12 < -72. Then, subtract 12 from both sides: 6n < -84. Finally, divide by 6: n < -14.

Front

When do you need to flip the inequality sign?

Back

You need to flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

What is the solution to the inequality -3x ≥ 12?

Back

To solve, divide both sides by -3 (flipping the sign): x ≤ -4.

Front

How do you graph the solution set of an inequality?

Back

To graph the solution set, draw a number line, use an open circle for < or > (not including) and a closed circle for ≤ or ≥ (including), and shade the appropriate direction.

Front

What is the solution to the inequality 3x - 5 > -26?

Back

Add 5 to both sides: 3x > -21. Then divide by 3: x > -7.

Front

What does the inequality 2n + 4 < 16 represent?

Back

To solve, subtract 4 from both sides: 2n < 12. Then divide by 2: n < 6.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary value, while a non-strict inequality (≤ or ≥) includes the boundary value.

Front

How do you check your solution for an inequality?

Back

Substitute a value from the solution set back into the original inequality to see if it holds true.

Front

What is the importance of isolating the variable in an inequality?

Back

Isolating the variable helps to clearly identify the range of values that satisfy the inequality.