Check #5 PAR. 2.1 Study Guide

Which expression is equivalent to the following: 4(5a + 3b - 6)?

• 20a + 3b - 6

• 20a + 12b - 24

• 9a + 7b - 2

• 5a + 12b - 24

• I don't know.

Answer explanation

To simplify 4(5a + 3b - 6), distribute 4: 4*5a + 4*3b + 4*(-6) = 20a + 12b - 24. Thus, the equivalent expression is 20a + 12b - 24.

Tags

CCSS.6.EE.A.4

Which expression is equivalent to the expression below? 3x + 5y - 2 + 2x - y + 4

• 5x + 4y + 2

• 5x + 4y - 2

• 5x + 4y + 6

• 5x + 4y

Answer explanation

To simplify the expression 3x + 5y - 2 + 2x - y + 4, combine like terms: (3x + 2x) + (5y - y) + (-2 + 4) = 5x + 4y + 2. Thus, the equivalent expression is 5x + 4y + 2.

Tags

CCSS.6.EE.A.4

Which expression is equivalent to 9.6 + 4t - 2.3 - 7t?

• 7.3 - 3t

• 11.9t

• 7.3 + 3t

• 7.3 - t

Answer explanation

To simplify 9.6 + 4t - 2.3 - 7t, combine like terms: 9.6 - 2.3 = 7.3 and 4t - 7t = -3t. Thus, the expression simplifies to 7.3 - 3t, which matches the correct answer.

Tags

CCSS.6.EE.A.4

Which expression represents the perimeter, in units, of this trapezoid?

• A. 17x + 25

• B. 42x

• C. 25x + 17

• D. 17x - 25

Answer explanation

The perimeter of a trapezoid is the sum of all its sides. The expression 17x + 25 correctly represents this sum, making it the right choice. Other options do not accurately reflect the total length of the sides.

Tags

CCSS.3.MD.D.8

Which is equivalent to the expression below? 5b + 3 - 2b + 8

• 3b + 11

• 7b + 11

• 3b + 5

• 7b + 5

Answer explanation

To simplify the expression 5b + 3 - 2b + 8, combine like terms: (5b - 2b) + (3 + 8) = 3b + 11. Thus, the equivalent expression is 3b + 11.

Tags

CCSS.6.EE.A.4

Which is equivalent to the expression below? 2m + 5 + 4m + 7 + 2n

• 6m + 2n + 12

• 6m + 12n

• 8m + n + 12

• 14m + 2n

Answer explanation

Combine like terms: 2m + 4m = 6m, and 5 + 7 = 12. The term 2n remains unchanged. Thus, the expression simplifies to 6m + 2n + 12, which matches the first answer choice.

Tags

CCSS.6.EE.A.4

• y + 3

Answer explanation

To find the equivalent expression, distribute \(\frac{2}{5}\) to both terms in \(y + 15\): \(\frac{2}{5}y + \frac{2}{5} \cdot 15 = \frac{2}{5}y + 6\). Thus, the correct choice is \(\frac{2}{5}y + 6\).

Tags

CCSS.6.EE.A.4

Simplify the following algebraic expression to its simplest form: 8x - 3 + 2x + 7

• 10x + 4

• 6x + 10

• 10x - 10

• 6x - 4

Answer explanation

Combine like terms: 8x + 2x = 10x and -3 + 7 = 4. Thus, the expression simplifies to 10x + 4, which is the correct answer.

Tags

CCSS.7.EE.A.1

What expression is equivalent to 5(x + 7)?

• 5x + 7

• 5x + 12

• 5x + 35

• 5x + 57

Answer explanation

To simplify 5(x + 7), distribute 5: 5 * x + 5 * 7 = 5x + 35. Thus, the expression equivalent to 5(x + 7) is 5x + 35.

Tags

CCSS.6.EE.A.4

Expand the expression.
-4(2x + 9)

• -8x + 9

• -8x - 36

• 8x + 9

• 8x - 36

Answer explanation

To expand -4(2x + 9), distribute -4: -4 * 2x = -8x and -4 * 9 = -36. Combine these results to get -8x - 36, which matches the correct answer.

Tags

CCSS.6.EE.A.3