Question 1

Solve for $$r in $$the equation $$8r - 2(r + 5) = 5(2r - 6) - 8.$$

Accepted Answer

$$r = -3$$

Question 2

Solve for $$x in $$the equation $$\frac{2}{7}(x-5) = -2 + \frac{2}{5}x.$$

Accepted Answer

$$x = 10$$

Question 3

Given $$P = 2l + 2w$$, solve for $$l in $$terms of $$P$$ and $$w.$$

Accepted Answer

$$l = \frac{P - 2w}{2}$$

Question 4

Solve the compound inequality $$4 \leq -3x + 1 \u003c 7$$ and express the solution in interval notation.

Accepted Answer

$$(-2, -1]$$

Question 5

Which of the following is the correct solution set for $$6x - 2  9$$?

Accepted Answer

$$x  3$$

Question 6

Three subtracted from five times a number is thirty-seven. What is the number?

Accepted Answer

$$x = 8$$

Question 7

A sheet of metal with an area of 30 square feet will be formed into a box 6 feet long by 1.5 feet wide. Using $$A = 2lw + 2lh + 2wh$$, what is the height $$h of $$the box?

Accepted Answer

$$h = 1$$

Question 8

Which of the following is the slope of the line passing through the points $$(1, 3)$$ and $$(-2, -9)$$?

Accepted Answer

$$m = 4$$

Question 9

What is the slope-intercept equation of the line parallel to $$y = \frac{1}{3}x + 6$$ that passes through the point $$(2, -1)$$?

Accepted Answer

$$y = \frac{1}{3}x - \frac{5}{3}$$

Question 10

Which of the following relations is NOT a function?

Accepted Answer

{$$(2, 2), (-18, 5), (3, -6), (2, 15), (-9, 3)$$}

Question 11

Evaluate $$f(3)$$ for $$f(x) = 4x + 3.$$

Accepted Answer

$$15$$

Question 12

Given the line $$y = 2x - 1$$, what is the slope and $$y-$$intercept?

Accepted Answer

Slope: $$2$$, $$y-$$intercept: $$-1$$

Question 13

Which of the following is the point-slope equation for a line with slope $$3$$ passing through $$(3, -5)$$?

Accepted Answer

$$y + 5 = 3(x - 3)$$

Question 14

Which of the following best describes the graph of $$y = -\frac{4}{5}x - 1$$?

Accepted Answer

A line with slope $$-\frac{4}{5}$$ and $$y-$$intercept $$-1$$

Question 15

If $$g(x) = \frac{x-4}{x^2$-9}$$, what is $$g(3)$$?

Accepted Answer

$$-\frac{1}{0} ($$undefined)

Question 16

Which of the following best describes the solution to $$y \geq -4x + 6$$ when graphed?

Accepted Answer

The region above the line $$y = -4x + 6$$, including the line

Question 17

Which of the following is the slope-intercept equation of the line perpendicular to $$y = \frac{1}{2}x - 7$$ that passes through $$(-1, 5)$$?

Accepted Answer

$$y = -2x + 3$$

Question 18

Which of the following is the correct interval notation for the solution to $$x - y \u003c 2$$?

Accepted Answer

All points below the line $$y = x - 2$$

Intermediate Algebra Exam Study Guide: Step-by-Step Guidance

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