Q: A chemist needs 14 liters of a 50% acid solution using only 40% and 70% solutions. Let $$x be $$the amount of 40% solution used. Which equation models this scenario?

$$0.4x + 0.7(14 - x) = 0.5 \times 14$$

Q: A technician mixes 500 mL of 50% alcohol with $$x mL of 70$$% alcohol to get a 65% solution. Which equation models this?

$$0.5 \times 500 + 0.7x = 0.65(500 + x)$$

Question 1

Which of the following is a linear equation in one variable?

Accepted Answer

$$5y - y = 2$$

Question 2

Solve the equation $$2x + 6 = 0$$ and select the correct solution set.

Accepted Answer

$$\{-3\}$$

Question 3

Which property of equality justifies the step from $$a = b to$$ $$a + c = b + c$$?

Accepted Answer

Addition Property of Equality

Question 4

A chemist needs 14 liters of a 50% acid solution using only 40% and 70% solutions. Let $$x be $$the amount of 40% solution used. Which equation models this scenario?

Accepted Answer

$$0.4x + 0.7(14 - x) = 0.5 	imes 14$$

Question 5

Solve the absolute value equation $$|x + 1| + 3 = 5.$$

Accepted Answer

$$x = 1 or$$ $$x = -3$$

Question 6

Which of the following represents the solution to $$x - 3 \u003c 7 in $$interval notation?

Accepted Answer

$$(-\infty, 10)$$

Question 7

A rectangular field's length is four times its width. If the perimeter is 500 yards, which equation models the width $$w$$?

Accepted Answer

$$2(w + 4w) = 500$$

Question 8

Solve the compound inequality $$-4 \leq 2x + 1 \leq 7$$ and express the solution in interval notation.

Accepted Answer

$$[-2.5, 3]$$

Question 9

A pair of running shoes costs $80. The store offers a 25% discount. What is the sale price?

Accepted Answer

$$60$$

Question 10

If $$|x| = -2$$, what is the solution set?

Accepted Answer

No solution

Question 11

Which of the following is an identity equation?

Accepted Answer

$$4(x + 3) = 2x + 18$$

Question 12

A smartphone originally costs $$800 but is now sold for 680. $$What is the percent decrease in price?

Accepted Answer

$$15\%$$

Question 13

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

Accepted Answer

$$x = -\frac{5}{8}$$

Question 14

Which of the following is the correct formula for simple interest?

Accepted Answer

$$I = PRT$$

Question 15

If $$|3x + 4| = |-2x + 7|$$, which equations should you solve?

Accepted Answer

$$3x + 4 = -2x + 7$$ and $$3x + 4 = 2x - 7$$

Question 16

A technician mixes 500 mL of 50% alcohol with $$x mL of 70$$% alcohol to get a 65% solution. Which equation models this?

Accepted Answer

$$0.5 	imes 500 + 0.7x = 0.65(500 + x)$$

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