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Select ALL of the expressions that are equivalent to

4(x+3)−10+6x


(1 point)
Responses

10x−7
10 x minus 7

−2x−7
negative 2 x minus 7

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

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

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
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1 answer

To determine which expressions are equivalent to \( 4(x + 3) - 10 + 6x \), let's simplify the original expression step by step.

  1. Distribute the 4: \[ 4(x + 3) = 4x + 12 \] So the expression becomes: \[ 4x + 12 - 10 + 6x \]

  2. Combine the constants and the terms with \( x \): \[ 12 - 10 = 2 \] Therefore, the expression simplifies to: \[ 4x + 6x + 2 = 10x + 2 \]

Now, the simplified expression is \( 10x + 2 \).

Next, we will compare this with the responses provided:

  1. \( 10x - 7 \): Not equivalent.
  2. \( -2x - 7 \): Not equivalent.
  3. \( 2(5x + 1) \): Let's simplify this. \[ 2(5x + 1) = 10x + 2 \text{ (this is equivalent)} \]
  4. \( 2(8x + 1) \): Let's simplify this. \[ 2(8x + 1) = 16x + 2 \text{ (not equivalent)} \]
  5. \( 4x + 3 - 10 + 6x \): Let's combine like terms from this expression. \[ 4x + 6x + 3 - 10 = 10x - 7 \text{ (not equivalent)} \]
  6. \( 4x + 12 - 10 + 6x \): The calculations here should match our original. \[ 4x + 6x + 2 = 10x + 2 \text{ (this is equivalent)} \]

Thus, the expressions that are equivalent to \( 4(x + 3) - 10 + 6x \) are:

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

Final answer:

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