Question 1

Solve for $$x$$: $$9x - 5 = 7 + 4x$$

Accepted Answer

$$x = \dfrac{12}{5}$$

Question 2

Which of the following is the solution to $$3(7x - 5) - 6(x - 9) = 5x + 12$$?

Accepted Answer

$$x = 8$$

Question 3

Solve for $$x$$: $$2x(x + 3) = 3(x^2$ + 2x)$$

Accepted Answer

$$x = 0 or$$ $$x = 9$$

Question 4

Which value of $$x$$ satisfies $$\dfrac{5}{3x - 6} = \dfrac{2}{x - 2}$$?

Accepted Answer

$$x = 4$$

Question 5

Simplify: $$(6 + 5i) - (8 - 6i)$$

Accepted Answer

$$-2 + 11i$$

Question 6

Simplify: $$\sqrt{8} (\sqrt{3} - \sqrt{7})$$

Accepted Answer

$$2\sqrt{6} - 2\sqrt{14}$$

Question 7

Simplify: $$(-4 + 2i) + (4 + 8i)$$

Accepted Answer

$$0 + 10i$$

Question 8

Solve for $$x$$ using the square root property: $$6x^2 = 150$

Accepted Answer

$$x = \pm 5$$

Question 9

Solve the equation by completing the square: $$x^2 + 7x + 4 = 0$

Accepted Answer

$$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$$

Question 10

Solve the equation using the quadratic formula: $$x^2 - 2x + 26 = 0$

Accepted Answer

$$x = 1 \pm 5i$$

Question 11

Solve for $$x$$: $$4x - 3x^2$ = 0$$

Accepted Answer

$$x = 0 or$$ $$x = 4$$

Question 12

Solve for $$x$$: $$(x + 35$$)^{3/2}$$ = 512$$

Accepted Answer

$$x = 29$$

Question 13

Solve the inequality and give the interval notation: $$6x + 5 \leq 4x + 19$$

Accepted Answer

$$(-\infty, 7]$$

Question 14

Solve the inequality and give the interval notation: $$-55 \u003c 3x + 13 \leq 34$$

Accepted Answer

$$(-6, 7]$$

Question 15

Solve the inequality and give the interval notation: $$6x - 5 \geq 8 or$$ $$6x - 5 \leq -8$$

Accepted Answer

$$(-\infty, -\dfrac{1}{3}] \cup [\dfrac{13}{6}, \infty)$$

Question 16

A chemist needs to prepare a solution by mixing two solutions: one with 10% acid and another with 30% acid. If she wants 100 mL of a 25% acid solution, how many mL of the 30% solution should she use?

Accepted Answer

$$75 mL$$

Question 17

A ball is thrown upward from the ground with an initial velocity of $$40 m/s. $$Its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -4.9t^2$ + 40t. $$After how many seconds will the ball reach its maximum height?

Accepted Answer

$$t = 4.08 s$$

Question 18

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$P = 20$$ thousand dollars

College Algebra: Solving Equations, Simplifying Expressions, and Solving Inequalities

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