Simplify 3 - (4x - 5) + 6.

Question

Responses.
A 12x + 2112x + 21
B 4x + 144x + 14
C 4x + 44x + 4
D -4x + 14-4x + 14
E -4x + 4

Answer 1

To simplify the expression \( 3 - (4x - 5) + 6 \):

1. Start by simplifying the term in parentheses: \[ 3 - (4x - 5) + 6 = 3 - 4x + 5 + 6 \]

2. Combine like terms: \[ 3 + 5 + 6 = 14 \] So, we have: \[ -4x + 14 \]

Thus, the simplified form of the expression is: \[ -4x + 14 \]

The correct response is D: -4x + 14.

Answer 2

Simplify: 9(a + b) + 4(3a + 2b)
Responses
A 13a 13b13a 13b
B 21a + 17b21a + 17b
C 21a + 2b21a + 2b
D 38ab

Answer 3

To simplify the expression \( 9(a + b) + 4(3a + 2b) \):

1. Distribute in the first term: \[ 9(a + b) = 9a + 9b \]

2. Distribute in the second term: \[ 4(3a + 2b) = 4 \cdot 3a + 4 \cdot 2b = 12a + 8b \]

3. Combine all the terms: \[ 9a + 9b + 12a + 8b = (9a + 12a) + (9b + 8b) = 21a + 17b \]

Thus, the simplified form of the expression is: \[ 21a + 17b \]

The correct response is B: 21a + 17b.

Answer 4

An expression is given.

(2x – 1) – 3.25(x + 3)

Which expression is equivalent to the given expression?

Responses
A -1.25x – 4.00-1.25 x – 4.00
B -1.25x - 3.25-1.25 x - 3.25
C -1.25x + 10.75-1.25 x + 10.75
D -1.25x - 10.75

Answer 5

To simplify the expression \( (2x - 1) - 3.25(x + 3) \):

1. Distribute \( -3.25 \) to the terms in the parentheses: \[ -3.25(x + 3) = -3.25x - 3.25 \times 3 = -3.25x - 9.75 \]

2. Substitute this back into the expression: \[ (2x - 1) - (3.25x + 9.75) = 2x - 1 - 3.25x - 9.75 \]

3. Combine like terms:

   • For the \( x \) terms: \[ 2x - 3.25x = -1.25x \]
   • For the constant terms: \[ -1 - 9.75 = -10.75 \]

Thus, putting it all together, we have: \[ -1.25x - 10.75 \]

The equivalent expression is: \[ -1.25x - 10.75 \]

The correct response is D: -1.25x - 10.75.

Answer 6

Which expression is equivalent to

1/4x − 36?
Responses
A

1/4 (x + 144)
B

1/4 (x − 144)
C

1/4 (x − 9)
D 4x − 9

Answer 7

To determine which expression is equivalent to \( \frac{1}{4}x - 36 \), we can start by factoring.

1. Notice that \( -36 \) can be rewritten in terms of \( \frac{1}{4} \): \[ -36 = -\frac{144}{4} \]

2. Now, we can rewrite the original expression: \[ \frac{1}{4}x - 36 = \frac{1}{4}x - \frac{144}{4} \]

3. Combine the terms over a common denominator: \[ \frac{1}{4}x - \frac{144}{4} = \frac{1}{4}(x - 144) \]

Thus, the equivalent expression is: \[ \frac{1}{4}(x - 144) \]

The correct response is B: \(\frac{1}{4}(x - 144)\).