Question

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

4(x+3)−10+6x


(2 points)
Responses

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

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

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

10x −7
10x −7

−2x−7

Answer 1

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

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

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

So, the simplified form of the expression \(4(x+3) - 10 + 6x\) is \(10x + 2\).

Now let's check each option to see if they also simplify to \(10x + 2\):

1. **Option 1:**
\[
4x + 12 - 10 + 6x
\]
This simplifies to \(10x + 2\) (same as ours).

2. **Option 2:**
\[
2(5x + 1)
\]
This simplifies to \(10x + 2\) (same as ours).

3. **Option 3:**
\[
4x + 3 - 10 + 6x
\]
This simplifies to \(10x - 7\), which is not equal to ours.

4. **Option 4:**
\[
2(8x + 1)
\]
This simplifies to \(16x + 2\), which is not equal to ours.

5. **Option 5:**
\[
10x - 7
\]
This is not equal to ours.

6. **Option 6:**
\[
-2x - 7
\]
This is not equal to ours.

The two expressions that are equivalent to \(4(x+3)-10+6x\) are:

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