Question 1

Which of the following equations is a first-degree equation with one unknown?

Accepted Answer

$2x + 5 = 9$

Question 2

A chemist is preparing a solution and needs to solve for $x$ in the equation $5x - 7 = 3x + 9$. What is the value of $x$?

Question 3

Which property of equivalent equations justifies the step from $a - 6.2 = -3.5$ to $a = 2.7$?

Accepted Answer

Adding the same number to both sides

Question 4

A medical researcher is tracking the dosage of a drug in a patient's bloodstream. The equation $0.25d + 5 = 10$ models the amount of drug $d$ (in mg) needed. What is the correct value of $d$?

Accepted Answer

$d = 25$

Question 5

Solve for $x$ in the equation $3(x - 4) = 2x + 5$. What is the solution?

Accepted Answer

$x = 7$

Question 6

Which of the following best describes a linear equation with one unknown?

Accepted Answer

An equation with only one variable and the variable's exponent is 1

Question 7

A business calculates its profit $P$ using the equation $P = 2x - 150$, where $x$ is the number of units sold. If the profit is $250$, how many units were sold?

Accepted Answer

$x = 200$

Question 8

Which step is necessary to solve the equation $\frac{1}{5}x = 7$?

Accepted Answer

Multiply both sides by 5

Question 9

A car rental company charges a flat fee of $\$50$ plus $\$0.20$ per mile driven. If the total cost is $\$90$, how many miles were driven?

Accepted Answer

$250$

Question 10

Solve for $x$: $4x - 7 = 2x + 5$

Accepted Answer

$x = 6$

Question 11

Which of the following equations has no solution?

Accepted Answer

$3x - 5 = 3x + 2$

Question 12

A biologist is studying the growth of bacteria and models the population with the equation $n + 250 = 3n$. What is the value of $n$ when the population triples?

Question 13

Which of the following is always true for any real number $x$?

Accepted Answer

$2x = 2x$

Question 14

A student solves the equation $2(x - 3) = 4x + 8$ and gets $x = -7$. Which of the following steps is correct in the solution process?

Accepted Answer

Distribute the 2 to get $2x - 6$

Question 15

Solve for $x$: $\frac{2x}{3} = 8$

Accepted Answer

$x = 12$

Question 16

Which of the following is NOT a valid step when solving $x + 5 = 3x + 4$?

Accepted Answer

Add $5$ to both sides

Question 17

A patient receives a prescription where the total daily dose $D$ in mg is given by $D = 4m + 10$, where $m$ is the number of pills. If the total dose is $50$ mg, how many pills should the patient take?

Accepted Answer

$m = 10$

Question 18

If $a = b$, which of the following is also true according to the properties of equivalent equations?

Accepted Answer

$a - c = b - c$

Question 19

A company’s revenue $R$ is modeled by $R = 12x - 300$, where $x$ is the number of products sold. If the revenue is $900$, how many products were sold?

Linear Equations and First-Degree Equations with One Unknown

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