$$a + (b \times c) = (a + b) \times c$$

Question 1

Which of the following is the coefficient in the term $$7x$$?

Accepted Answer

$$7$$

Question 2

What is the constant term in the expression $$4x + 9y + 12$$?

Accepted Answer

$$12$$

Question 3

Which of the following pairs are like terms?

Accepted Answer

$$5x$$ and $$8x$$

Question 4

Using the commutative property of addition, which expression is equivalent to $$a + 7$$?

Accepted Answer

$$7 + a$$

Question 5

Which property justifies the equation $$(x + 2) + 5 = x + (2 + 5)$$?

Accepted Answer

Associative Property of Addition

Question 6

Simplify the expression $$3(2x + 4) + 5x.$$

Accepted Answer

$$11x + 12$$

Question 7

Which of the following demonstrates the distributive property?

Accepted Answer

$$a(b + c) = ab + ac$$

Question 8

Combine like terms in the expression $$8y + 3x + 2y + 7x.$$

Accepted Answer

Question 9

Simplify the expression $$5(2x + 3) + 4x.$$

Accepted Answer

$$14x + 15$$

Question 10

A chemist mixes two solutions: $$3x mL of $$solution A and $$7x mL of $$solution B. What is the total volume in terms of $$x$$?

Accepted Answer

$$10x$$

Question 11

Which of the following is NOT a correct application of the associative property?

Accepted Answer

$$a + (b 	imes c) = (a + b) 	imes c$$

Question 12

Simplify the expression $$7(4x + 3y) + 2(5x + y).$$

Accepted Answer

$$38x + 23y$$

Question 13

Which step should be performed first when simplifying $$6(2x + 5) + 4x$$?

Accepted Answer

Apply the distributive property

Question 14

A company’s profit is modeled by $$P = 8x + 12 - 3x. $$What is the simplified expression for profit?

Accepted Answer

$$5x + 12$$

Question 15

Which of the following is a correct use of the commutative property of multiplication?

Accepted Answer

$$ab = ba$$

Question 16

Simplify the expression $$2x + 8 + 5x + 7.$$

Accepted Answer

$$7x + 15$$

Question 17

Which of the following is the best description of 'like terms'?

Accepted Answer

Terms with the same variable part

Question 18

A medical researcher records the number of patients as $$4x + 7 + 3x. $$What is the simplified expression for the total number of patients?

Accepted Answer

$$7x + 7$$

Question 19

Which property allows you to rewrite $$6(5x) as$$ $$(6 \cdot 5)x$$?

Accepted Answer

Associative Property of Multiplication

Question 20

Simplify the expression $$9a - 4a + 2(3a + 1).$$

Accepted Answer

$$11a + 2$$

Chapter 1: Variables, Real Numbers, and Mathematical Models – Basic Rules of Algebra

Study Guide - Practice Questions