Question 1

A chemist is preparing a solution and needs to solve for $$x in $$the equation $$9x - 5 = 7 + 4x. $$What is the value of $$x$$?

Accepted Answer

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

Question 2

A company is comparing two pricing models given by $$3(7x - 5) - (6x - 9) = 5x + 12. $$What is the solution for $$x$$?

Accepted Answer

$$x = \dfrac{19}{10}$$

Question 3

Solve for $$x in $$the equation $$2x(x + 3) = 3(x^2$ + 2x)$$, which models the intersection of two parabolic paths.

Accepted Answer

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

Question 4

A biologist is modeling population growth with the equation $$\dfrac{5}{3x-6} = \dfrac{2}{x-2}. $$What is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 5

Simplify the expression $$(6 + 5i) - (8 - 6i)$$, where $$i is $$the imaginary unit.

Accepted Answer

$$-2 + 11i$$

Question 6

Simplify $$\sqrt{8} (\sqrt{3} - \sqrt{7})$$ and choose the correct answer.

Accepted Answer

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

Question 7

A physicist is analyzing a complex number calculation: $$(-4 + 2i)(4 + 3i). $$What is the simplified result?

Accepted Answer

$$-22 + i$$

Question 8

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

Accepted Answer

$$x = \pm 5$$

Question 9

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

Accepted Answer

$$x = -1 \pm 5i$$

Question 11

Solve the equation $$4x - 3x^2$ = 0$$ for $$x.$$

Accepted Answer

$$x = 0 or$$ $$x = 1$$

Question 12

Solve the inequality $$6x + 5 \u003e 4x + 19$$ and express the solution in interval notation.

Accepted Answer

$$(7, \infty)$$

Question 13

Solve the compound inequality $$-5 \u003c 3x + 13 \u003c 34$$ and express the solution in interval notation.

Accepted Answer

$$(-6, 7)$$

Question 14

Solve the absolute value inequality $$|6x - 5| \geq 8$$ and express the solution in interval notation.

Accepted Answer

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

Question 15

A business is analyzing profit using the equation $$x^2 - 2x + 21 = 0$. What are the solutions for x$?

Accepted Answer

$$x = 1 \pm 4.58i$$

Question 16

Solve for $$x in $$the equation $$(x + 35$$)^{3/2}$$ = 512.$$

Accepted Answer

$$x = 93$$

Question 17

A medical researcher is modeling the spread of a virus with the equation $$x^2 + 7x + 4 = 0$. What is the solution for x$?

Accepted Answer

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

Question 18

Solve the equation $$3x + 7 = 9$$ for $$x.$$

Accepted Answer

$$x = 2$$

Question 19

Solve the inequality $$72 + 4x \u003c 18$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -13.5)$$

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

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