Q: Which of the following is a correct application of the multiplication property of equality?

If $$a = b$$ and $$c \neq 0$$, then $$ac = bc$$

Question 1

Which property allows you to multiply both sides of an equation by the same nonzero number without changing the solution?

Accepted Answer

The Multiplication Property of Equality

Question 2

Solve for $$x in $$the equation $$5x = 35.$$

Accepted Answer

$$x = 7$$

Question 3

Solve for $$y in $$the equation $$-8y = 56.$$

Accepted Answer

$$y = -7$$

Question 4

What is the solution to the equation $$-x = 12$$?

Accepted Answer

$$x = -12$$

Question 5

Solve for $$x in $$the equation $$\frac{1}{3}x = 9.$$

Accepted Answer

$$x = 27$$

Question 6

Solve for $$x in $$the equation $$-\frac{1}{4}x = 5.$$

Accepted Answer

$$x = -20$$

Question 7

A formula for the price $$P of a $$purebred Westie puppy is $$P = 18n + 765$$, where $$n is $$the number of years after 1940. What is the price predicted by the formula in 2009?

Accepted Answer

$$P = 2007$$

Question 8

If the price of a Westie puppy reaches $$2151$$, in what year does the formula $$P = 18n + 765$$ predict this will occur?

Accepted Answer

2017

Question 9

Solve for $$x in $$the equation $$2x + 5 = -15.$$

Accepted Answer

$$x = -10$$

Question 10

Which of the following steps is necessary to solve $$-x = c$$ for $$x$$?

Accepted Answer

Multiply both sides by $$-1$$

Question 11

A chemical reaction requires the temperature $$T (in $$degrees Celsius) to be three times the number of grams $$g of a $$substance. If the temperature is $$60^{\circ}C$$, how many grams of the substance are present?

Accepted Answer

$$g = 20$$

Question 12

Solve for $$x in $$the equation $$7x - 14 = 0.$$

Accepted Answer

$$x = 2$$

Question 13

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

$$200$$

Question 14

Solve for $$x in $$the equation $$\frac{2}{5}x = 8.$$

Accepted Answer

$$x = 20$$

Question 15

If $$-x = -9$$, what is the value of $$x$$?

Accepted Answer

$$x = 9$$

Question 16

A historical event occurred 77 years after 1940. In what year did it occur?

Accepted Answer

2017

Question 17

Solve for $$x in $$the equation $$4x + 8 = 0.$$

Accepted Answer

$$x = -2$$

Question 18

A medication dosage is calculated by the formula $$D = 2w + 5$$, where $$D is $$the dosage in mg and $$w is $$the patient's weight in kg. If a patient receives a $$45 mg $$dose, what is their weight?

Accepted Answer

$$w = 20$$

Question 19

Which of the following is a correct application of the multiplication property of equality?

Accepted Answer

If $$a = b$$ and $$c 
eq 0$$, then $$ac = bc$$

Question 20

Solve for $$x in $$the equation $$-3x = 15.$$

Accepted Answer

$$x = -5$$

Solving Linear Equations and Inequalities in One Variable

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