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

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

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: $-55 < 3x + 13 \leq 34$

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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