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

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

Question 1

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

Accepted Answer

$$5y - y = 2$$

Question 2

Which equation matches the general form of a linear equation in one variable?

Accepted Answer

$$ax + b = c$$

Question 3

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

Accepted Answer

$$x = -3$$

Question 4

Which of the following is NOT a linear equation in one variable?

Accepted Answer

$$x^2 = 25$

Question 5

A number decreased by 7 is equal to 15. What is the number?

Accepted Answer

$$x = 22$$

Question 6

Which property of equality justifies the following step: If $$a = b$$, then $$a + c = b + c$$?

Accepted Answer

Addition Property of Equality

Question 7

Solve for $$m in $$the equation $$\frac{2m}{3} + 8 = 12.$$

Accepted Answer

$$m = 6$$

Question 8

Translate and solve: Seven more than twice a number is equal to 19.

Accepted Answer

$$2x + 7 = 19; x = 6$$

Question 9

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

Accepted Answer

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

Question 10

If a smartphone originally costs $$800 but is now sold for 680$$, what is the percent decrease in price?

Accepted Answer

$$15\%$$

Question 11

Solve the inequality $$x - 3 \u003c 7$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, 10)$$

Question 12

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

Accepted Answer

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

Question 13

A patient’s medication dose was increased by 15% to 23 cc. What was the original dose?

Accepted Answer

$$20 cc$$

Question 14

Which of the following is an identity equation?

Accepted Answer

$$5y - y = 4y$$

Question 15

A team of geologists uses the formula $$P = 0.025d to $$estimate pressure $$P (in $$MPa) at depth $$d (in $$meters). What is the pressure at 120 meters?

Accepted Answer

$$3$$ MPa

Question 16

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

Accepted Answer

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

Question 17

A square garden has sides of 8 ft. The gardener reduces each side by 1 ft. What is the percent decrease in the perimeter?

Accepted Answer

$$12.5\%$$

Question 18

Which of the following is the correct translation for: 'The quotient of a number and 6 subtracted from 9 is equal to 1'?

Accepted Answer

$$9 - \frac{x}{6} = 1$$

Question 19

If $$-5.4 + c = 1.6$$, what is the value of $$c$$?

Accepted Answer

$$c = 7$$

Identifying Linear Equations in One Variable

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