Question 1

A chemist is mixing two solutions, one with a concentration of $$x$$ mol/L and another with a concentration of $$2x$$ mol/L. If the total concentration after mixing is $$9$$ mol/L, and the chemist used $$5 L of $$the first solution and $$7 L of $$the second, what is the value of $$x$$?

Accepted Answer

$$x = 3.5$$

Question 2

Solve for $$x$$: $$3(7x - 5) - 6(x - 9) = 5x + 12$$

Accepted Answer

$$x = 8$$

Question 3

A biologist is studying the growth of a bacteria population modeled by $$x^2 + 13x = 40$. What are the possible values for x$?

Accepted Answer

$$x = -8, x = 5$$

Question 4

Simplify the following expression: $$(6 + 5i) - (8 - 6i)$$

Accepted Answer

$$-2 + 11i$$

Question 5

A medical researcher is analyzing a quadratic equation for the spread of a virus: $$x^2 + 7x + 4 = 0$. Solve by completing the square.

Accepted Answer

$$x = -\frac{7}{2} \pm \frac{\sqrt{29}}{2}$$

Question 6

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

Accepted Answer

$$x = 1 \pm 5i$$

Question 7

A company’s profit is modeled by the equation $$6x^2 = 150$. What are the possible values of x$?

Accepted Answer

$$x = \pm 5$$

Question 8

Solve for $$x$$: $$x^2 - 2x = 96$

Accepted Answer

$$x = 1 \pm \sqrt{97}$$

Question 9

A physicist is analyzing the motion of a particle and models its position with $$x^2 + 4x - 5 = 0$. What are the solutions for x$?

Accepted Answer

$$x = -5, x = 1$$

Question 10

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

Accepted Answer

$$x \geq \frac{13}{6}$$

Question 11

A population model is given by $$x^2 + 7x + 26 = 0$. What are the solutions for x$?

Accepted Answer

$$x = -\frac{7}{2} \pm \frac{\sqrt{29}}{2}i$$

Question 12

Solve for $$x$$: $$x^2 - 10x = 0$

Accepted Answer

$$x = 0, x = 10$$

Question 13

A business is analyzing its break-even point using the equation $$4x - 3x^2$ = 0. $$What are the possible values for $$x$$?

Accepted Answer

$$x = 0, x = 4$$

Question 14

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

Accepted Answer

$$(-6, 7]$$

Question 15

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

Accepted Answer

$$0 + 10i$$

Question 16

Solve for $$x$$: $$x^2 + 4x = 0$

Accepted Answer

$$x = 0, x = -4$$

Question 17

A physicist is analyzing a projectile’s motion and models its height with $$x^2 + 7x + 26 = 0$. What is the nature of the solutions?

Accepted Answer

Two complex solutions

Question 18

Solve for $$x$$: $$x^2 - 49 = 0$

Accepted Answer

$$x = 7, x = -7$$

Question 19

Solve the inequality and give the interval notation: $$6x - 5 \leq 8 or$$ $$6x - 5 \geq 13$$

Accepted Answer

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

Question 20

A chemical reaction is modeled by $$x^2 + 35x = 51x$. What are the possible values for x$?

Accepted Answer

$$x = 0, x = 16$$

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

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