Q: A chemist needs to prepare 100 mL of a 30% saline solution by mixing a 20% solution and a 50% solution. Let $$x be $$the amount (in mL) of the 20% solution used. Which equation models this scenario?

$$0.20x + 0.50(100 - x) = 0.30 \times 100$$

Question 1

Which of the following best defines a linear equation in one variable?

Accepted Answer

An equation where the variable appears only in the first power and can be written in the form $$ax + b = c.$$

Question 2

What is the main reason you should never divide both sides of a linear equation by an expression containing the variable you are solving for?

Accepted Answer

It may eliminate valid solutions or introduce extraneous solutions.

Question 3

Given the equation $$5x - 7 = 18$$, what is the solution for $$x$$?

Accepted Answer

$$x = 5$$

Question 4

Which of the following is NOT a step in the formal process for solving a linear equation?

Accepted Answer

Multiply both sides by zero.

Question 5

If the solution set of an equation is $$\{3\}$$, which statement is true?

Accepted Answer

The equation has exactly one solution, $$x = 3.$$

Question 6

A chemist needs to prepare 100 mL of a 30% saline solution by mixing a 20% solution and a 50% solution. Let $$x be $$the amount (in mL) of the 20% solution used. Which equation models this scenario?

Accepted Answer

$$0.20x + 0.50(100 - x) = 0.30 	imes 100$$

Question 7

Which of the following best describes the domain of a variable in an equation?

Accepted Answer

The set of all possible values the variable can assume.

Question 8

Solve for $$x$$: $$\frac{2x}{3} + 4 = 10$$

Accepted Answer

$$x = 6$$

Question 9

Which operation would you perform first to solve the equation $$7x + 5 = 26$$?

Accepted Answer

Subtract 5 from both sides.

Question 10

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If your total bill was $$\65$, how many miles did you drive?

Accepted Answer

$$200$$ miles

Question 11

Which of the following is an equivalent equation to $$3x - 4 = 11$$?

Accepted Answer

$$3x = 15$$

Question 12

What is the solution set for the equation $$2(x - 3) = 4$$?

Accepted Answer

$$\{5\}$$

Question 13

Which step comes first when solving an applied problem, according to the provided steps?

Accepted Answer

Read the problem carefully and identify what you are looking for.

Question 14

If $$4x + 9 = 17$$, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 15

Which of the following is a correct step when clearing fractions in a linear equation?

Accepted Answer

Multiply both sides by the least common denominator.

Solving Linear Equations and Applied Problems in College Algebra

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