Question

Select the two expression that are equivalent to the given expression.
4 ( x + 3) - 10 + 6x


2 ( 8x + 1)

2 ( 5x + 1)

4x + 12 - 10 + 6x

4x + 3 - 10 + 6x

-2x - 7

10x - 7

Answer 1

Let's simplify the given expression step by step:

The expression is:
\[ 4(x + 3) - 10 + 6x \]

1. Distribute \(4\) into \((x + 3)\):
\[ 4x + 12 - 10 + 6x \]

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

Now we have simplified the given expression to \(10x + 2\).

Next, we will evaluate which of the provided options are equivalent to \(10x + 2\):

1. **Option 1: \(2(8x + 1)\)**
- Simplifying this:
\[ 2(8x + 1) = 16x + 2 \]
- Not equivalent.

2. **Option 2: \(2(5x + 1)\)**
- Simplifying this:
\[ 2(5x + 1) = 10x + 2 \]
- Equivalent.

3. **Option 3: \(4x + 12 - 10 + 6x\)**
- This is the same expression we simplified earlier.
- Combining like terms gives \(10x + 2\), so it is equivalent.

4. **Option 4: \(4x + 3 - 10 + 6x\)**
- Simplifying this:
\[ 4x + 6x + 3 - 10 = 10x - 7 \]
- Not equivalent.

5. **Option 5: \(-2x - 7\)**
- Not equivalent.

6. **Option 6: \(10x - 7\)**
- Not equivalent.

The two expressions that are equivalent to the given expression \(10x + 2\) are:
- **2 ( 5x + 1)**
- **4x + 12 - 10 + 6x**