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 $$x$$?

Accepted Answer

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?

Accepted Answer

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?

Accepted Answer

Linear Equations and First-Degree Equations with One Unknown

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