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 -4x + 14 ≤ 54?

Back

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

Front

What does the solution a > 6 represent on a number line?

Back

The solution a > 6 represents all numbers greater than 6, which is shown on a number line as an open circle at 6 and a line extending to the right.

Front

How do you graph the solution set of the inequality -4a ≤ -28?

Back

To graph -4a ≤ -28, first divide by -4 (flipping the inequality sign) to get a ≥ 7. Then, plot a closed circle at 7 and shade to the right.

Front

What is the first step in solving the inequality 28 - k ≥ 7(k - 4)?

Back

The first step is to distribute the 7 on the right side: 28 - k ≥ 7k - 28.

Front

What does the inequality k ≤ 7 indicate about the variable k?

Back

The inequality k ≤ 7 indicates that k can take any value less than or equal to 7.

Front

What is the importance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign when dividing by a negative number is crucial because it maintains the truth of the inequality.

Front

What is the solution set of the inequality a ≥ 4?

Back

The solution set of a ≥ 4 includes all numbers greater than or equal to 4, represented on a number line with a closed circle at 4 and shading to the right.

Front

How do you isolate the variable in the inequality 3x + 5 < 20?

Back

To isolate x in 3x + 5 < 20, subtract 5 from both sides to get 3x < 15, then divide by 3 to find x < 5.

Front

What is the graphical representation of the solution to the inequality x > 2?

Back

The graphical representation of x > 2 is an open circle at 2 with a line extending to the right.