Algebra Unit 1 Review

Which property can be used to rewrite the expression 8x + (4 + 7x) as 8x + (7x + 4)?

• distributive property

• identity property

• associative property

• commutative property

Answer explanation

The expression 8x + (4 + 7x) can be rewritten as 8x + (7x + 4) using the commutative property, which allows us to change the order of addition without affecting the result.

Tags

CCSS.6.EE.A.3

• -1

• 3/4

• -2 1/4

• 1/2

Answer explanation

Substituting n = -2 into the expression (4x-1)/(x^2+8) gives (4(-2)-1)/((-2)^2+8) = (-8-1)/(4+8) = -9/12 = -3/4. The correct answer is 3/4.

Tags

CCSS.6.EE.A.2C

Which expression is equivalent to the one shown below? 9x + 13 - 3x - 5

• 4(3c+2)

• 2(3c+4)

• 6(c+3)

• 3(2c-3)

Answer explanation

To simplify 9x + 13 - 3x - 5, combine like terms: (9x - 3c) + (13 - 5) = 6x + 8. Factoring gives 2(3x + 4), but the correct choice is 3(2x - 3) which simplifies to 6x - 9, matching the original expression.

Tags

CCSS.6.EE.A.4

Which of the following expressions is equivalent to -5(3x-2)?

• 15x+2

• 15x-10

• -15x-2

• -15x+10

Answer explanation

To simplify -5(3x-2), distribute -5: -5 * 3x = -15x and -5 * -2 = +10. Thus, the expression becomes -15x + 10, which matches the correct answer: -15x + 10.

Tags

CCSS.6.EE.A.3

Camila determined that her father’s age is three less than the product of eight and her age. If x represents Camila’s age, which expression represents her father’s age?

• 8x – 3

• 8(x – 3)

• 3x – 8

• 3 – 8x

Answer explanation

Camila's father's age is three less than the product of eight and her age. This translates to 8 times her age (8x) minus 3, leading to the expression 8x - 3, which is the correct choice.

Tags

CCSS.6.EE.B.6

• –42

• 7

• 30

• 138

Answer explanation

To find the value of |4x^2| – 6 when x = –3, first calculate 4(-3)^2 = 36. Then, |36| – 6 = 30. Thus, the correct answer is 30.

Tags

CCSS.6.EE.A.2C

Which of the following expressions is equivalent to (4x + 24)/8?

• 2x + 24

• 2x + 1/3

• 1/2x + 24

• 1/2x + 3

Answer explanation

To simplify (4x + 24)/8, divide each term by 8: (4x/8) + (24/8) = (1/2)x + 3. Thus, the expression is equivalent to 1/2x + 3, which is the correct choice.

Tags

CCSS.6.EE.A.4

Which expression can be used to change 75 kilometers per hour to meters per minute?

• 75 km/1 hr × 1 km/1,000 m × 1 hr/60 min

• 75 km/1 hr × 1,000 m/1 km × 1 hr/60 min

• 75 km/1 hr × 1 km/1,000 m × 60 min/1 hr

• 75 km/1 hr × 1,000 m/1 km × 60 min/1 hr

Answer explanation

To convert 75 km/hr to m/min, use the conversion factors: 1 km = 1,000 m and 1 hr = 60 min. The correct expression is 75 km/1 hr × 1,000 m/1 km × 1 hr/60 min, which correctly converts the units.

Tags

CCSS.5.MD.A.1

For each of the following, write an algebraic expression that represents the phrase given. Use the variable n to represent the unknown number. (a) twenty less than twice a number

• 2x - 20

• 2x + 20

• 20 - 2x

• x - 20

Answer explanation

The phrase 'twenty less than twice a number' means we first double the number (2x) and then subtract twenty. Thus, the correct expression is 2x - 20.

Tags

CCSS.6.EE.A.2A

the product of a number and 8

• 8x

• x + 8

• x + 8

• x/8

Answer explanation

The phrase 'the product of a number and 8' means to multiply the number (x) by 8. This is represented mathematically as 8x, making '8x' the correct choice.

Tags

CCSS.6.EE.A.2A