Question 1

Which of the following is TRUE about solving inequalities?

Accepted Answer

You reverse the inequality sign when multiplying or dividing both sides by a negative number.

Question 2

Solve the inequality $$4x \u003c -4$$ and choose the correct solution.

Accepted Answer

$$x \u003c -1$$

Question 3

What is the solution to $$-2x \geq 6$$?

Accepted Answer

$$x \leq 3$$

Question 4

Which operation requires you to reverse the direction of the inequality sign?

Accepted Answer

Multiplying both sides by a negative number

Question 5

Solve and graph: $$4x + 1 \u003c -3. $$What is the solution?

Accepted Answer

$$x \u003c -2$$

Question 6

If you multiply both sides of the inequality $$a \u003c b by$$ $$-2$$, what is the resulting inequality?

Accepted Answer

$$-2a \u003e -2b$$

Question 7

Which of the following is the correct first step to solve $$4x - 6 \u003e x - 5$$?

Accepted Answer

Subtract $$x$$ from both sides

Question 8

Solve the inequality $$7 - 3x \leq 19.$$

Accepted Answer

$$x \leq -4$$

Question 9

Which of the following best describes the solution set for $$x \u003e -2 on a $$number line?

Accepted Answer

All numbers to the right of $$-2$$, not including $$-2$$

Question 10

A real-world scenario: A company requires that the temperature in a storage room must be less than $$4^	ext{o}C. $$Which inequality represents this requirement if $$T is $$the temperature?

Accepted Answer

$$T \u003c 4$$

Question 11

Which step is necessary before solving for the variable in an inequality?

Accepted Answer

Combine like terms and remove parentheses

Question 12

If $$x$$ represents the number of hours worked and the minimum wage law requires at least $$15$$ hours per week, which inequality represents this situation?

Accepted Answer

$$x \geq 15$$

Question 13

Solve the inequality $$5 - 2x \geq 11.$$

Accepted Answer

$$x \leq -3$$

Question 14

Which of the following is a common mistake when solving inequalities?

Accepted Answer

Forgetting to reverse the inequality sign when multiplying by a negative number

Question 15

If $$x is a $$solution to $$-2x \geq 6$$, which of the following must also be true?

Accepted Answer

$$x is $$less than or equal to $$3$$

Solving and Graphing Linear Inequalities

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