2-step Inequalities

Front

What is a 2-step inequality?

Back

A 2-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -9a - 1 < 26?

Back

To solve -9a - 1 < 26, first add 1 to both sides to get -9a < 27, then divide by -9 (remember to flip the inequality sign) to find a > -3.

Front

What does the solution a > -3 represent in terms of a number line?

Back

The solution a > -3 represents all numbers greater than -3 on the number line, which is shown as an open circle at -3 and a line extending to the right.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

To solve -4x + 14 ≤ 54, subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (flipping the inequality sign) to find x ≥ -10.

Front

What is the significance of the inequality sign in x ≥ -10?

Back

The inequality sign in x ≥ -10 indicates that x can be -10 or any number greater than -10.

Front

How do you interpret the inequality -4x + 5 ≤ 29?

Back

To interpret -4x + 5 ≤ 29, solve for x by subtracting 5 from both sides to get -4x ≤ 24, then divide by -4 (flipping the sign) to find x ≥ -6.

Front

What does the inequality 106 - 4x ≤ 70 represent in a real-world context?

Back

The inequality 106 - 4x ≤ 70 represents the weight of Casey's dog decreasing by 4 pounds per week until it reaches a maximum weight of 70 pounds.

Front

How do you graph the solution to the inequality x ≥ -6?

Back

To graph x ≥ -6, place a closed circle on -6 (indicating -6 is included) and shade the line to the right to show all numbers greater than -6.

Front

What is the first step in solving a 2-step inequality?

Back

The first step in solving a 2-step inequality 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

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.