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

4(x+3)−10+6x

(2 points)
Responses

4x+12−10+6x

−2x−7

2(5x+1)

10x −7

2(8x+1)

4x+3−10+6x

1 answer

To find the two expressions that are equivalent to \( 4(x+3)-10+6x \), let's first simplify the given expression step by step.

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

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

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

Now, we see that the original expression simplifies to \( 10x + 2 \).

Next, let's analyze the response options to see which ones are equivalent to \( 10x + 2 \).

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

    • This simplifies to \( 10x + 2 \), which is equivalent.

  2. \( -2x - 7 \)

    • This is not equivalent.

  3. \( 2(5x + 1) \)

    • This simplifies to \( 10x + 2 \), which is equivalent.

  4. \( 10x - 7 \)

    • This is not equivalent.

  5. \( 2(8x + 1) \)

    • This simplifies to \( 16x + 2 \), which is not equivalent.

  6. \( 4x + 3 - 10 + 6x \)

    • This simplifies to \( 10x - 7 \), which is not equivalent.

Thus, the TWO expressions that are equivalent to the original expression are:

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