Topic 3 Study Guide

Elijah has n apples and buys 7 more. Write an algebraic expression to represent the number of apples he now has.
(a)  

• Total Apples

• n + 7
• n

• 7

Answer explanation

Elijah starts with n apples and buys 7 more. To find the total, we add the apples he had (n) to the apples he bought (7), resulting in n + 7. Thus, the correct answer is n + 7.

Tags

CCSS.6.EE.A.2

• 5

• 3

• 8

Answer explanation

In the expression 5x + 3, the coefficient is the number that multiplies the variable x. Here, 5 is the coefficient of x, making the correct answer 5.

Tags

CCSS.6.EE.A.2B

• 10 cents

• 8 cents

• 6 cents

• 12 cents

Answer explanation

To find the cost of each pencil, substitute x = 2 into the expression 3x + 4. This gives 3(2) + 4 = 6 + 4 = 10 cents. Therefore, Nora pays 10 cents.

Tags

CCSS.6.EE.A.2C

Answer explanation

To simplify the expression 2(x + 3), distribute the 2: 2 * x + 2 * 3 = 2x + 6. Thus, the equivalent expression is 2x + 6, which is the correct choice.

Tags

CCSS.6.EE.A.3

Answer explanation

To simplify the expression, combine like terms: 4a + 3a = (4 + 3)a = 7a. Therefore, the correct answer is 7a.

Tags

CCSS.6.EE.A.3

Answer explanation

The terms in the expression 7x + 5y - 3 are the individual components separated by '+' or '-'. Thus, the correct choice is 7x, 5y, -3, as these represent the full terms in the expression.

Tags

CCSS.6.EE.A.2B

• 27

• 30

• 33

• 36

Answer explanation

To evaluate the expression 2x^2 + 3x for x = 3, substitute 3 into the expression: 2(3^2) + 3(3) = 2(9) + 9 = 18 + 9 = 27. The correct answer is 33, which is incorrect; the correct evaluation is 27.

Tags

CCSS.6.EE.A.2C

Answer explanation

To simplify the expression 3(x + 4) + 2x, first distribute: 3x + 12 + 2x. Then combine like terms: 3x + 2x = 5x. Thus, the equivalent expression is 5x + 12, which is the correct choice.

Tags

CCSS.6.EE.A.3

• Yes

• No

• Sometimes

• Cannot be determined

Answer explanation

The expression 4(x + 2) simplifies to 4x + 8 by distributing the 4. Since both expressions represent the same value for any x, they are equivalent. Therefore, the correct answer is Yes.

Tags

CCSS.6.EE.A.4

Answer explanation

To factor the expression 6x + 9, we can find the greatest common factor, which is 3. Dividing both terms by 3 gives us 3(2x + 3), making this the correct choice.

Tags

CCSS.6.EE.A.3