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

Study Guide - Practice Questions