Question 1

Solve the equation $$2x - 6 = -10 + 5x. $$What is the value of $$x$$?

Accepted Answer

$$x = -\dfrac{3}{4}$$

Question 2

Which of the following is the solution set to the compound inequality $$6x + 12  8$$?

Accepted Answer

$$(-\infty, -6) \cup (5, \infty)$$

Question 3

How many real solutions does the equation $$x^2$$ \cdot $$(x^2 - 1) = 0$ have?

Accepted Answer

3

Question 4

Solve the quadratic equation $$x^2 - 7x + 10 = 0$.

Accepted Answer

$$x = 5,\ x = 2$$

Question 5

If the discriminant of a quadratic equation is $$49$$, how many real solutions does it have?

Accepted Answer

two

Question 6

Solve the equation $$(x + 1$$)^{3/2}$$ = 27$$ for $$x.$$

Accepted Answer

8

Question 7

Find the solution set to the compound inequality $$3 \u003c -2x + 1 \leq 5.$$

Accepted Answer

$$( -2, -1 ]$$

Question 8

Solve the absolute value inequality $$|x - 2| \geq 8.$$

Accepted Answer

$$(-\infty, -6] \cup [10, \infty)$$

Question 9

Solve the absolute value inequality $$|x - 2| \geq -8.$$

Accepted Answer

$$(-\infty, \infty)$$

Question 10

Given the formula $$y = mx + b$$, solve for $$m in $$terms of $$x$$, $$y$$, and $$b.$$

Accepted Answer

$$m = \dfrac{y - b}{x}$$

Question 11

A medical laboratory uses the equation $$\sqrt{7x + 18} = x to $$determine the concentration $$x of a $$substance in a blood sample. What is the solution for $$x$$?

Accepted Answer

$$x = 6$$

Question 12

Solve for $$x in $$the equation $$|2x - 1| = |-2x - 1|.$$

Accepted Answer

$$x = 0$$

Question 13

A company models its profit with the quadratic equation $$x^2 + 4x + 1 = 0$. What are the solutions for x$?

Accepted Answer

$$x = -2 \pm \sqrt{3}$$

Question 14

Solve the equation $$2(-6x + 2) + 4 = -5(x - 1)$$ for $$x.$$

Accepted Answer

$$x = 2$$

Question 15

A chemical reaction is modeled by the equation $$3x^3$$ = $$24x^2. $$What are all real solutions for $$x$$?

Accepted Answer

Question 16

Solve the rational equation $$\left( \dfrac{1}{x} \$$right)^2$$ - \dfrac{1}{x} - 2 = 0$$ for $$x.$$

Accepted Answer

$$x = 1,\ x = -2$$

Question 17

Solve the absolute value equation $$|4x + 5| = 11$$ for $$x.$$

Accepted Answer

$$x = 1.5,\ x = -4$$

Question 18

Solve the inequality $$x^2 - x - 2$$ \u003c 0$$ and express your answer in interval notation.

Accepted Answer

$$(-1, 2)$$

Question 19

A business uses the formula $$y = mx + b to $$predict sales. If $$x = 1$$, $$y = 2$$, and $$b = 3$$, what is the value of $$m$$?

Accepted Answer

$$m = -1$$

College Algebra Practice Exam Guidance

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