Question 1

Solve the compound inequality $$x + 11 \geq 3$$ and $$7x - 12 \geq 2. $$What is the solution set in interval notation?

Accepted Answer

$$[2, \infty)$$

Question 2

Which of the following best describes the solution set to $$x + 11 \geq 3$$?

Accepted Answer

$$[-8, \infty)$$

Question 3

What is the solution to $$7x - 12 \geq 2 in $$interval notation?

Accepted Answer

$$[2, \infty)$$

Question 4

What is the intersection of the solution sets $$x \geq -8$$ and $$x \geq 2$$?

Accepted Answer

$$[2, \infty)$$

Question 5

If a compound inequality is formed by the word "and," what does the solution set represent?

Accepted Answer

The intersection of the solution sets

Question 6

Solve for $$x$$: $$x + 11 \geq 3. $$What is the first step?

Accepted Answer

Subtract 11 from both sides

Question 7

Which of the following is the correct solution to $$7x - 12 \geq 2$$?

Accepted Answer

$$x \geq \frac{2 + 12}{7}$$

Question 8

Given the inequalities $$x + 11 \geq 3$$ and $$7x - 12 \geq 2$$, which value of $$x$$ satisfies both?

Accepted Answer

$$x = 2$$

Question 9

If the solution to $$x + 11 \geq 3 is$$ $$x \geq -8$$ and the solution to $$7x - 12 \geq 2 is$$ $$x \geq 2$$, what is the graphical representation of their intersection?

Accepted Answer

A number line shaded from $$2 to$$ $$\infty$$

Question 10

Which real-world scenario could be modeled by the compound inequality $$x + 11 \geq 3$$ and $$7x - 12 \geq 2$$?

Accepted Answer

A temperature range for a chemical reaction that must satisfy two safety standards

Question 11

If $$x$$ represents the number of hours worked and the inequalities $$x + 11 \geq 3$$ and $$7x - 12 \geq 2$$ must both be satisfied, what is the minimum number of hours that meets both requirements?

Accepted Answer

$$2$$

Question 12

Which step is necessary to solve $$7x - 12 \geq 2$$ for $$x$$?

Accepted Answer

Add 12 to both sides, then divide by 7

Question 13

If the solution to a compound inequality is $$[2, \infty)$$, which of the following values is NOT in the solution set?

Accepted Answer

$$1$$

Question 14

Which of the following best describes the meaning of the interval notation $$[2, \infty)$$?

Accepted Answer

All real numbers greater than or equal to 2

Question 15

If $$x$$ must satisfy both $$x \geq -8$$ and $$x \geq 2$$, what is the smallest integer value $$x$$ can take?

Accepted Answer

$$2$$

Solving Compound Inequalities and Expressing Solutions in Interval Notation

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