Q: A chemist needs 14 liters of a 50% acid solution using 40% and 70% solutions. If $$x is $$the liters of 40% solution, which equation models the problem?

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

Question 1

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

Accepted Answer

$$2x + 6 = 0$$

Question 2

Solve the equation $$2x + 6 = 0$$ for $$x.$$

Accepted Answer

$$x = -3$$

Question 3

Which of the following is an expression, not an equation?

Accepted Answer

$$2x + 6$$

Question 4

A number decreased by 7 is equal to 15. Which equation represents this statement?

Accepted Answer

$$x - 7 = 15$$

Question 5

Which property of equality would you use to solve $$x - 6 = 0$$?

Accepted Answer

Addition Property of Equality

Question 6

Solve for $$m in $$the equation $$\frac{2m}{3} + 8 = 10.$$

Accepted Answer

$$m = 3$$

Question 7

Translate and solve: 'Three times a number is 54.'

Accepted Answer

$$3x = 54;\ x = 18$$

Question 8

Which of the following equations has no solution?

Accepted Answer

$$x + 5 = x + 7$$

Question 9

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 10

A chemist needs 14 liters of a 50% acid solution using 40% and 70% solutions. If $$x is $$the liters of 40% solution, which equation models the problem?

Accepted Answer

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

Question 11

Solve the inequality $$3x - 5 \u003c 7.$$

Accepted Answer

$$x \u003c 4$$

Question 12

Which of the following is the solution to $$|x + 1| = 5$$?

Accepted Answer

$$x = 4 or$$ $$x = -6$$

Question 13

A store offers a 25% discount on shoes originally priced at $80. What is the sale price?

Accepted Answer

$$60$$

Question 14

If $$|2x - 3| \u003c 7$$, what is the solution set for $$x$$?

Accepted Answer

$$-2 \u003c x \u003c 5$$

Question 15

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

Accepted Answer

$$20 cc$$

Question 16

Which of the following is the correct interval notation for the solution to $$x - 3 \u003c 7$$?

Accepted Answer

$$(-\infty, 10)$$

Question 17

If the average of five numbers is 79, and the first four are 82, 75, 80, and 77, what is the fifth number?

Accepted Answer

$$81$$

Question 18

A city’s population grew from 120,000 to 138,000 in one year. What is the percent increase?

Accepted Answer

$$15\%$$

Question 19

Solve the compound inequality $$-4 \leq 2x + 1 \leq 7.$$

Accepted Answer

$$-2.5 \leq x \leq 3$$

Question 20

Which of the following is the solution to $$|x| = |y|$$?

Accepted Answer

$$x = y or$$ $$x = -y$$

Solving Linear Equations: Properties of Equality and Applications

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