Question

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

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

10x −7
10x −7

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

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

−2x−7
negative 2 x minus 7
Skip to navigation

Answer 1

To find which two expressions are equivalent to the given expression \( 4(x+3)−10+6x \), we first need to simplify the original expression:

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

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

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

Now, we are looking for expressions that simplify to \( 10x + 2 \):

1. **Check \( 4x + 12 - 10 + 6x \)**:
- We already simplified this in the steps above to get \( 10x + 2 \).
- **This is equivalent.**

2. **Check \( 10x - 7 \)**:
- This does not match \( 10x + 2 \).
- **This is not equivalent.**

3. **Check \( 2(8x + 1) \)**:
- Distributing gives \( 2 \cdot 8x + 2 \cdot 1 = 16x + 2 \).
- This does not match \( 10x + 2 \).
- **This is not equivalent.**

4. **Check \( 2(5x + 1) \)**:
- Distributing gives \( 2 \cdot 5x + 2 \cdot 1 = 10x + 2 \).
- **This is equivalent.**

5. **Check \( -2x - 7 \)**:
- This is clearly not equivalent to \( 10x + 2 \).
- **This is not equivalent.**

Thus, the two expressions that are equivalent to the given expression \( 4(x+3)−10+6x \) are:

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