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

Guida di studio - Domande di pratica

Study guide - Flashcard