Question 1

Which of the following is the correct solution to the linear equation $2x + 3 = 0$?

Accepted Answer

$x = -\dfrac{3}{2}$

Question 2

A chemist needs to dilute a solution so that the final concentration is 5%. If she has 100 mL of a 20% solution, how much water should she add to achieve the desired concentration? (Let $x$ be the amount of water added in mL.)

Accepted Answer

$x = 300$

Question 3

Solve for $x$ in the equation $\dfrac{3x - 6}{8} = 5 - \dfrac{1}{4}(x - 4)$.

Accepted Answer

$x = 8$

Question 4

A patient is prescribed a medication that requires the dosage to be calculated by the formula $D = 2w + 5$, where $D$ is the dosage in mg and $w$ is the patient's weight in kg. If the patient weighs 70 kg, what is the correct dosage?

Accepted Answer

$D = 145$ mg

Question 5

Which of the following is the solution to the equation $\dfrac{4x + 3}{4} = 2x - x$?

Accepted Answer

$x = -3$

Question 6

A business has fixed costs of $\$500$ and variable costs of $\$20$ per unit produced. If the total cost is $\$900$, how many units were produced?

Accepted Answer

$20$

Question 7

Solve for $x$: $\dfrac{x}{2} + \dfrac{x}{3} = 5$

Question 8

Which of the following is the correct solution to the quadratic equation $x^2 - 6x + 8 = 0$?

Accepted Answer

$x = 2$ or $x = 4$

Question 9

A car rental company charges a flat fee of $\$50$ plus $\$0.20$ per mile driven. If a customer paid $\$90$, how many miles did they drive?

Accepted Answer

$200$

Question 10

Solve for $x$ in the equation $x^2 = 3x + 18$.

Accepted Answer

$x = 6$ or $x = -3$

Question 11

A biologist is studying a population that doubles every year. If the initial population is 100, after how many years will the population reach 800?

Accepted Answer

$4$

Question 12

Which of the following is the correct solution to $x^2 - 4x - 5 = 0$?

Accepted Answer

$x = 5$ or $x = -1$

Question 13

A pharmacist needs to mix a 10% saline solution with a 30% saline solution to obtain 100 mL of a 25% solution. How many mL of the 30% solution should be used?

Accepted Answer

$75$ mL

Question 14

Solve for $x$ in the equation $x^2 + 3x - 18 = 0$.

Accepted Answer

$x = 3$ or $x = -6$

Question 15

A company’s revenue $R$ (in dollars) is given by $R = 50x - 200$, where $x$ is the number of units sold. If the company wants to break even (i.e., $R = 0$), how many units must be sold?

Question 16

Which of the following is the correct solution to $x^2 + 3x - 18 = 0$?

Accepted Answer

$x = 3$ or $x = -6$

Question 17

A student borrows $\$500$ at an annual simple interest rate of 6%. How much will the student owe after 3 years?

Accepted Answer

$\$590$

Question 18

Solve for $x$ in the equation $\dfrac{2x + 3}{4} = \dfrac{x - 2}{2}$.

Accepted Answer

$x = 7$

Question 19

A rectangle has a length that is 3 times its width. If the perimeter is 48 units, what is the area of the rectangle?

Accepted Answer

$216$

Question 20

Which of the following is the correct solution to $x^2 - 9 = 0$?

Accepted Answer

$x = 3$ or $x = -3$

Solving Linear and Quadratic Equations

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