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Question

Question
Select the TWO expressions that are equivalent to the given expression.

4(x+3)−10+6x


(2 points)
Responses

−2x−7
negative 2 x minus 7

4x+3−10+6x
4 x plus 3 minus 10 plus 6 x

4x+12−10+6x
4 x plus 12 minus 10 plus 6 x

2(5x+1)
2 times open paren 5 x plus 1 close paren

10x −7
10x −7

2(8x+1)
2 times open paren 8 x plus 1 close paren
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Answer 1

To determine which two expressions are equivalent to the given expression \(4(x + 3) - 10 + 6x\), let's simplify the original expression step-by-step:

1. Distribute the \(4\) into \((x + 3)\): \[ 4(x + 3) = 4x + 12 \]

2. Substitute this back into the expression: \[ 4x + 12 - 10 + 6x \]

3. Combine like terms: \[ 4x + 6x + 12 - 10 = 10x + 2 \]

Now we have simplified the original expression to \(10x + 2\).

Now, let's check which of the provided expressions are equivalent to \(10x + 2\):

1. \(-2x - 7\) - Not equivalent.
2. \(4x + 3 - 10 + 6x\): \[ 4x + 3 - 10 + 6x = 10x - 7 \quad (\text{Not equivalent.}) \]
3. \(4x + 12 - 10 + 6x\): \[ 4x + 12 - 10 + 6x = 10x + 2 \quad (\text{Equivalent!}) \]
4. \(2(5x + 1)\): \[ 2(5x + 1) = 10x + 2 \quad (\text{Equivalent!}) \]
5. \(10x - 7\) - Not equivalent.
6. \(2(8x + 1)\): \[ 2(8x + 1) = 16x + 2 \quad (\text{Not equivalent.}) \]

Thus, the two expressions that are equivalent to the original expression \(4(x + 3) - 10 + 6x\) are:

1. \(4x + 12 - 10 + 6x\)
2. \(2(5x + 1)\)