Question 1

Which of the following correctly rewrites $$|-345|$$ without absolute value bars?

Accepted Answer

$$345$$

Question 2

Rewrite $$|6 - 13|$$ without absolute value bars.

Accepted Answer

$$7$$

Question 3

What is the value of $$|-14|$$?

Accepted Answer

$$14$$

Question 4

Simplify $$-8 - (-14).$$

Accepted Answer

$$6$$

Question 5

Which inequality represents the interval $$(-8, -2]$$?

Accepted Answer

$$-8 \u003c x \leq -2$$

Question 6

Express the interval $$[7, \infty) in $$inequality notation.

Accepted Answer

$$x \geq 7$$

Question 7

Which inequality corresponds to the interval $$(-\infty, 1)$$?

Accepted Answer

$$x \u003c 1$$

Question 8

Write the interval $$(1, 3) in $$inequality notation.

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 9

Add and simplify $$\frac{13}{19} + \frac{3}{13}.$$

Accepted Answer

$$\frac{226}{247}$$

Question 10

Subtract and simplify $$\frac{13}{15} - \frac{2}{9}.$$

Accepted Answer

$$\frac{29}{45}$$

Question 11

Multiply and simplify $$\frac{10}{51} \cdot \frac{3}{8}.$$

Accepted Answer

$$\frac{5}{68}$$

Question 12

Compute and simplify $$\frac{4}{3} \div \frac{16}{9}.$$

Accepted Answer

$$\frac{3}{4}$$

Question 13

Evaluate $$3(x + y) - 5y$$ for $$x = 4$$ and $$y = -3.$$

Accepted Answer

$$18$$

Question 14

Evaluate $$x^2 + xy - 9y$ for x = 21$ and y = -15$.

Accepted Answer

$$-237$$

Question 15

A medical thermometer reads $$-8$$ degrees Celsius. If the temperature increases by $$14$$ degrees, what is the new temperature?

Accepted Answer

$$6$$ degrees

Question 16

A chemical reaction requires the temperature to be in the interval $$[7, \infty). $$Which of the following temperatures is NOT allowed?

Accepted Answer

$$6$$ degrees$

Question 17

A patient’s blood pressure must be less than $$1$$ unit for a certain medication. Which interval represents the allowed values?

Accepted Answer

$$(-\infty, 1)$$

Question 18

If a car’s speed must be between $$1$$ and $$3$$ mph (not including $$1 or$$ $$3$$), which interval notation represents this?

Accepted Answer

$$(1, 3)$$

Question 19

A scientist mixes two solutions: $$\frac{13}{19}$$ liters and $$\frac{3}{13}$$ liters. What is the total volume?

Accepted Answer

$$\frac{226}{247}$$ liters

Precalculus Foundations: Absolute Value, Intervals, and Arithmetic Guidance

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