Question 1

Solve the inequality $$3(8 - 2x) \geq 38 - 4x$$ and express the solution set in interval notation.

Accepted Answer

$$[7, \infty)$$

Question 2

Which of the following represents the correct interval notation for the solution set of $$3(8 - 2x) \geq 38 - 4x$$?

Accepted Answer

$$[7, \infty)$$

Question 3

After solving $$3(8 - 2x) \geq 38 - 4x$$, which of the following best describes the graph of the solution set on a number line?

Accepted Answer

A closed circle at $$x = 7$$ and shading to the right

Question 4

If the solution set to an inequality is $$[7, \infty)$$, which of the following statements is true?

Accepted Answer

All real numbers greater than or equal to 7 are solutions.

Question 5

Which step is necessary to isolate $$x in $$the inequality $$3(8 - 2x) \geq 38 - 4x$$?

Accepted Answer

Expand the left side and combine like terms

Question 6

What is the first step in solving $$3(8 - 2x) \geq 38 - 4x$$?

Accepted Answer

Distribute the 3 on the left side

Question 7

After distributing and simplifying $$3(8 - 2x) \geq 38 - 4x$$, what is the resulting inequality?

Accepted Answer

$$24 - 6x \geq 38 - 4x$$

Question 8

Which of the following is the correct next step after $$24 - 6x \geq 38 - 4x$$?

Accepted Answer

Add $$4x to $$both sides

Question 9

What is the solution to $$24 - 6x \geq 38 - 4x$$ after combining like terms?

Accepted Answer

$$-2x \geq 14$$

Question 10

When solving $$-2x \geq 14$$, what is the correct way to isolate $$x$$?

Accepted Answer

Divide both sides by $$-2$$ and reverse the inequality

Question 11

What is the final solution for $$-2x \geq 14$$?

Accepted Answer

$$x \geq 7$$

Question 12

Which of the following real-world scenarios could be modeled by the inequality $$3(8 - 2x) \geq 38 - 4x$$?

Accepted Answer

A company needs at least as much profit as its competitor, where $$x is $$the number of products sold.

Question 13

If the solution set is $$[7, \infty)$$, which of the following values of $$x is $$NOT included in the solution?

Accepted Answer

$$x = 6$$

Question 14

Which of the following is a common mistake when solving $$-2x \geq 14$$?

Accepted Answer

Not reversing the inequality when dividing by a negative number

Question 15

If the solution set to an inequality is $$[7, \infty)$$, how would you represent this on a number line?

Accepted Answer

A closed circle at 7 and shading to the right

Question 16

Which interval notation represents all real numbers greater than or equal to 7?

Accepted Answer

$$[7, \infty)$$

Question 17

What is the solution set for the inequality $$3(8 - 2x) \geq 38 - 4x$$?

Accepted Answer

$$[7, \infty)$$

Question 18

Which of the following is NOT a valid step in solving $$3(8 - 2x) \geq 38 - 4x$$?

Accepted Answer

Multiplying both sides by $$-1$$ without reversing the inequality

Question 19

If you graph the solution set $$[7, \infty) on a $$number line, which point is included?

Accepted Answer

$$x = 7$$

Solving Linear Inequalities and Expressing Solution Sets in Interval Notation

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