Question 1

Solve the compound inequality $$6x + 3 \leq -9$$ and $$5x \leq 0. $$What is the solution set in interval notation?

Accepted Answer

$$( -\infty, -2 ]$$

Question 2

Which of the following steps is necessary to isolate $$x in $$the inequality $$6x + 3 \leq -9$$?

Accepted Answer

Subtract 3 from both sides

Question 3

After simplifying $$6x + 3 \leq -9$$, what is the next step to solve for $$x$$?

Accepted Answer

Divide both sides by 6

Question 4

What is the solution to $$5x \leq 0$$?

Accepted Answer

$$x \leq 0$$

Question 5

Which of the following best describes the intersection of the solution sets for $$x \leq -2$$ and $$x \leq 0$$?

Accepted Answer

$$x \leq -2$$

Question 6

If a chemical process requires the temperature $$T (in$$ $$^\circC) to $$satisfy $$6T + 3 \leq -9$$ and $$5T \leq 0$$, what is the maximum allowable temperature?

Accepted Answer

$$-2$$ $$^\circC$$

Question 7

Which of the following is the correct process to solve $$6x + 3 \leq -9$$?

Accepted Answer

Subtract 3 from both sides, then divide both sides by 6

Question 8

A company must keep its pollution index $$x$$ such that $$6x + 3 \leq -9$$ and $$5x \leq 0. $$Which of the following values is acceptable for $$x$$?

Accepted Answer

$$-3$$

Question 9

Which of the following intervals represents all real numbers $$x$$ that satisfy both $$6x + 3 \leq -9$$ and $$5x \leq 0$$?

Accepted Answer

$$( -\infty, -2 ]$$

Question 10

If $$x$$ represents the dosage of a medication in mg, and it must satisfy $$6x + 3 \leq -9$$ and $$5x \leq 0$$, what is the highest safe dosage?

Accepted Answer

$$-2 mg$$

Question 11

Which of the following is NOT a solution to the compound inequality $$6x + 3 \leq -9$$ and $$5x \leq 0$$?

Accepted Answer

$$x = 0$$

Question 12

A historical event requires the year $$x to $$satisfy $$6x + 3 \leq -9$$ and $$5x \leq 0. $$Which year could $$x$$ represent?

Accepted Answer

$$-5$$

Question 13

Which of the following best describes the solution set for $$6x + 3 \leq -9$$?

Accepted Answer

$$x \leq -2$$

Question 14

If $$x$$ must satisfy both $$6x + 3 \leq -9$$ and $$5x \leq 0$$, which of the following is the correct way to write the solution set?

Accepted Answer

$$( -\infty, -2 ]$$

Solving Compound Inequalities in Intermediate Algebra

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