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 $|2x - 5| < 7$?

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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