Question 1

Solve the inequality $4(8 - 2x) \geq 28 - 6x$ and express the solution set in interval notation.

Accepted Answer

$(-\infty, 2]$

Question 2

Which graph correctly represents the solution set $(-\infty, 2]$ on a number line?

Accepted Answer

A ray extending left from 2, with a closed circle at 2

Question 3

If the solution set to an inequality is $(-\infty, 2]$, which of the following values is NOT included in the solution set?

Accepted Answer

$3$

Question 4

Given the inequality $4(8 - 2x) \geq 28 - 6x$, what is the first step to solve for $x$?

Accepted Answer

Distribute the 4 to both terms inside the parentheses

Question 5

After distributing and simplifying $4(8 - 2x) \geq 28 - 6x$, what is the resulting inequality?

Accepted Answer

$32 - 8x \geq 28 - 6x$

Question 6

Which of the following best describes the interval $(-\infty, 2]$?

Accepted Answer

All real numbers less than or equal to 2

Question 7

If a solution set is $\emptyset$, what does this mean?

Accepted Answer

There are no real solutions to the inequality

Question 8

Which of the following is the correct interval notation for all real numbers less than or equal to $a$?

Accepted Answer

$(-\infty, a]$

Question 9

Suppose you are solving $4(8 - 2x) \geq 28 - 6x$ for a chemical process where $x$ represents the temperature in degrees Celsius. What is the maximum allowable temperature for the process?

Accepted Answer

$2$ degrees Celsius

Question 10

Which of the following statements is true about the solution set $(-\infty, 2]$?

Accepted Answer

It includes all numbers less than or equal to 2

Question 11

If the solution set to an inequality is $(-\infty, 2]$, which of the following intervals is a subset of the solution set?

Accepted Answer

$(-5, 2]$

Question 12

A medical researcher is testing a drug that is only safe for patients with a body temperature $x$ such that $x \leq 2$. Which interval notation correctly represents the set of safe temperatures?

Accepted Answer

$(-\infty, 2]$

Question 13

Which of the following is NOT a correct way to write the solution set for $x \leq 2$?

Accepted Answer

$[2, \infty)$

Question 14

If the solution set is $(-\infty, 2]$, which of the following graphs best represents this set?

Accepted Answer

A number line shaded to the left of 2, with a closed circle at 2

Question 15

Which of the following is the correct solution to $4(8 - 2x) \geq 28 - 6x$ after all steps are completed?

Accepted Answer

$x \leq 2$

Solving Linear Inequalities and Expressing Solution Sets

Study Guide - Practice Questions

Study Guide - Flashcards