Let's first simplify the given expression:
\[ 4(x + 3) - 10 + 6x \]
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Distribute \(4\) into the parentheses: \[ 4x + 12 - 10 + 6x \]
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Combine like terms: \[ 4x + 6x + 12 - 10 = 10x + 2 \]
So the simplified expression is \(10x + 2\).
Now, let's evaluate the options:
a. \(2(5x + 1)\) \[ = 10x + 2 \] This is equivalent.
b. \(10x - 7\) This is NOT equivalent.
c. \(-2x - 7\) This is NOT equivalent.
d. \(4x + 12 - 10 + 6x\) \[ = 10x + 2 \] This is equivalent.
e. \(4x + 3 - 10 + 6x\) \[ = 4x + 6x + 3 - 10 = 10x - 7 \] This is NOT equivalent.
f. \(2(8x + 1)\) \[ = 16x + 2 \] This is NOT equivalent.
The two expressions that are equivalent to the original expression \(4(x+3)-10+6x\) are:
- a. \(2(5x + 1)\)
- d. \(4x + 12 - 10 + 6x\)