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

Question

4(x+3)−10+6x

(2 points)
Responses

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

10x −7
10x −7

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

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

−2x−7
negative 2 x minus 7
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Answer 1

To find which two expressions are equivalent to the given expression \( 4(x+3)−10+6x \), we first need to simplify the original expression:

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

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

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

Now, we are looking for expressions that simplify to \( 10x + 2 \):

1. Check \( 4x + 12 - 10 + 6x \):

   • We already simplified this in the steps above to get \( 10x + 2 \).
   • This is equivalent.

2. Check \( 10x - 7 \):

   • This does not match \( 10x + 2 \).
   • This is not equivalent.

3. Check \( 2(8x + 1) \):

   • Distributing gives \( 2 \cdot 8x + 2 \cdot 1 = 16x + 2 \).
   • This does not match \( 10x + 2 \).
   • This is not equivalent.

4. Check \( 2(5x + 1) \):

   • Distributing gives \( 2 \cdot 5x + 2 \cdot 1 = 10x + 2 \).
   • This is equivalent.

5. Check \( -2x - 7 \):

   • This is clearly not equivalent to \( 10x + 2 \).
   • This is not equivalent.

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

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