Question 1

Solve for $$x$$: $$5(x + 3) + 4x - 3 = 2(x - 4).$$

Accepted Answer

$$x = -7$$

Question 2

Solve for $$s$$: $$s = 9gt^2$ for t$ in terms of s$ and g$.

Accepted Answer

$$t = \sqrt{\dfrac{s}{9g}}$$

Question 3

Solve for $$m$$: $$F = \dfrac{Gm_1m_2}{r^2$}$$ for $$m_1.$$

Accepted Answer

$$m_1$$ = \dfrac{$$Fr^2$$}{$$Gm_2$$}$$

Question 4

Solve for $$h$$: $$S = 2\pi r h + 2\pi r^2$ for h$.

Accepted Answer

$$h = \dfrac{S - 2\pi r^2$}{2\pi r}$$

Question 5

Solve for $$a$$: $$a = ax - 3b + bx$$ for $$x.$$

Accepted Answer

$$x = \dfrac{a + 3b}{a + b}$$

Question 6

A square's side is increased by 3 cm. The perimeter of the new square is 40 cm more than twice the original square's perimeter. What is the length of the original square's side?

Accepted Answer

$$x = 11$$

Question 7

Simplify: $$\dfrac{1}{1 + \dfrac{1}{x}}.$$

Accepted Answer

$$\dfrac{x}{x + 1}$$

Question 8

Solve for $$x$$: $$-2x - x = -10.$$

Accepted Answer

$$x = 10/3$$

Question 9

Solve for $$x$$: $$x^2 - 2x + 1 = 0$.

Accepted Answer

$$x = 1$$

Question 10

Solve for $$x$$: $$\dfrac{3x^2$}{x - 2} + 1 = \dfrac{-2}{7 - 2x}.$$

Accepted Answer

$$x = 1 or$$ $$x = 2$$

Question 11

Solve for $$x$$: $$x = \sqrt{4x + 12}.$$

Accepted Answer

$$x = 6 or$$ $$x = -2$$

Question 12

Write the solution to $$3 - 4x \geq 2x + 8 in $$interval notation.

Accepted Answer

$$(-\infty, -\dfrac{5}{3}]$$

Question 13

Write the solution to $$x^2 - 2x - 15$$ \leq 0$$ in interval notation.

Accepted Answer

$$[-3, 5]$$

Question 14

Solve for $$x$$: $$17 - 3x = 3.$$

Accepted Answer

$$x = 4$$

Question 15

A chemist needs to prepare 100 mL of a 30% acid solution by mixing a 20% solution and a 50% solution. How many mL of the 50% solution should be used?

Accepted Answer

$$40 mL$$

Question 16

A ball is thrown upward from the ground with an initial velocity of $$20 m/s. $$Its height after $$t$$ seconds is given by $$h = -4.9t^2$ + 20t. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$2.04 s$$

Question 17

Which of the following is the solution set for $$|2x - 5| \u003c 7$$?

Accepted Answer

$$(-1, 6)$$

Question 18

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$17$$

Question 19

Which of the following is the solution to the system: $$\begin{cases} x + y = 5 \ 2x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 3)$$

Question 20

A population of bacteria triples every 4 hours. If the initial population is 500, what will the population be after 12 hours?

Accepted Answer

$$13,500$$

College Algebra: Solving Equations, Simplifying Expressions, and Interval Notation

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