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select the two expressions that are equivalent to the given expression

4(x+3)-10+6x
a. 2(5x+1)
b. 10x-7
c. -2x-7
d. 4x+12-10+6x
e. 4x+3 -10+6x
f. 2(8x+1)

1 answer

Let's first simplify the given expression:

\[ 4(x + 3) - 10 + 6x \]

  1. Distribute \(4\) into the parentheses: \[ 4x + 12 - 10 + 6x \]

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