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

4(x+3)−10+6x

(2 points)
Responses

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

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

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

−2x−7
negative 2 x minus 7

10x −7
10x −7

2(5x+1)

1 answer

Let's simplify the given expression step by step:

  1. Start with the expression: \[ 4(x + 3) - 10 + 6x \]

  2. Distribute the \(4\) over \((x + 3)\): \[ 4x + 12 - 10 + 6x \]

  3. Combine like terms:

    • Combine \(4x\) and \(6x\): \[ 4x + 6x = 10x \]
    • Now, combine \(12 - 10\): \[ 12 - 10 = 2 \]

Putting it all together, we have: \[ 10x + 2 \]

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

  1. \(4x + 3 - 10 + 6x\):

    • Simplifying this, we have \(4x + 6x = 10x\) and \(3 - 10 = -7\), so it results in \(10x - 7\) (not equivalent).

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

    • This expands to \(16x + 2\) (not equivalent).

  3. \(4x + 12 - 10 + 6x\):

    • Simplifying this, we get \(10x + 2\) (this is equivalent).

  4. \(-2x - 7\):

    • This represents \(-2x - 7\) (not equivalent).

  5. \(10x - 7\):

    • This is \(10x - 7\) (not equivalent).

  6. \(2(5x + 1)\):

    • This expands to \(10x + 2\) (this is equivalent).

Thus, the two equivalent expressions are:

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