Question 1

Solve the equation using the multiplication property of equality: $$\frac{59}{-8} = -10. $$What is the solution set?

Accepted Answer

$$\left\{ \frac{15}{4} \right\}$$

Question 2

Solve for $$k in $$the equation: $$8k - (7 + k) = -(6k + 7). $$What is the solution set?

Accepted Answer

$$\left\{ -1 \right\}$$

Question 3

Solve the equation and check your solution: $$\frac{19}{25} - r = -6. $$What is the solution set?

Accepted Answer

$$\left\{ \frac{169}{25} \right\}$$

Question 4

Solve the equation: $$2 + 1.5(z + 2) = 3.5z - 7. $$What is the solution set?

Accepted Answer

$$\left\{ 5 \right\}$$

Question 5

Determine whether the equation $$7(z + 8) = 6(z - 5) + z is a $$contradiction, an identity, or a conditional equation.

Accepted Answer

Conditional

Question 6

Solve for $$y in $$the equation $$9x - 3y = 6. $$What is $$y in $$terms of $$x$$?

Accepted Answer

$$y = 3x - 2$$

Question 7

Translate the statement into an equation: 'Triple the sum of a number and 7 is the same as 4 more than the number.' Let $$x$$ represent the unknown number.

Accepted Answer

$$3(x + 7) = x + 4$$

Question 8

A 59-inch piece of wire is cut into three pieces. The shortest piece is 5 inches shorter than the middle piece, and the longest piece is 4 inches longer than the middle piece. Which equation models the total length if $$x is $$the length of the middle piece?

Accepted Answer

$$x + (x - 5) + (x + 4) = 59$$

Question 9

After Mrs. Fisher lost 7% of her investment, she had $20,925 left. What was her original investment amount?

Accepted Answer

$$22,500$$

Question 10

The length of a rectangle is 8 feet longer than its width. If the perimeter is 116 feet, what is the width?

Accepted Answer

$$25$$

Question 11

Two boats leave a port at the same time, one going north at 61 mph and the other south at 43 mph. How many hours until they are 1352 miles apart?

Accepted Answer

$$13$$

Question 12

Solve the inequality and express the solution in interval notation: $$3n - 5(n - 3) \u003c 2n - 17.$$

Accepted Answer

$$(8, \infty)$$

Question 13

Solve the inequality $$-3y - 33 \u003c 5$$ and express the solution in set-builder notation.

Accepted Answer

$$\{ y \mid y \u003e -12.67 \}$$

Question 14

Find the slope of the line passing through the points $$(2, -6)$$ and $$(-2, -2). $$What does the slope represent?

Accepted Answer

$$-1$$; y$ decreases by 1 for every increase of 1 in x

Question 15

What is the slope and y-intercept of the line $$x - 4y = 8$$?

Accepted Answer

Slope: $$\frac{1}{4}$$, y-intercept: $$-2$$

Question 16

Find the equation of the line with an undefined slope and x-intercept $$(-5, 0). $$What is the equation?

Accepted Answer

$$x = -5$$

Question 17

Determine if the lines $$y - x = -2$$ and $$y + x = 3$$ are parallel, perpendicular, or neither.

Accepted Answer

Perpendicular

Question 18

Find the equation of the line that passes through $$(2, 1)$$ and is perpendicular to $$x - 3y = -5. $$Write your answer in slope-intercept form.

Accepted Answer

$$y = -3x + 7$$

Question 19

Solve the system by graphing: $$y = -x + 2$$ and $$y = x + 4. $$What is the solution?

Accepted Answer

$$( -1, 3 )$$

Step-by-Step Guidance for College Algebra Exam Review

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