Question

Which of the following expressions is equivalent to 3x + 3x + 5 + 5?

3( x + 5)
2(6 x + 10)
2(3 x + 5)
3( x + 10)

Answer 1

Let's simplify the expression \(3x + 3x + 5 + 5\):

1. Combine the like terms \(3x + 3x\):
\[
3x + 3x = 6x
\]

2. Combine the constants \(5 + 5\):
\[
5 + 5 = 10
\]

Thus, we have:
\[
3x + 3x + 5 + 5 = 6x + 10
\]

Now, we can look for an equivalent expression from the provided options:

1. **Option 1:** \(3(x + 5)\)
\[
= 3x + 15 \quad \text{(not equivalent)}
\]

2. **Option 2:** \(2(6x + 10)\)
\[
= 12x + 20 \quad \text{(not equivalent)}
\]

3. **Option 3:** \(2(3x + 5)\)
\[
= 6x + 10 \quad \text{(equivalent)}
\]

4. **Option 4:** \(3(x + 10)\)
\[
= 3x + 30 \quad \text{(not equivalent)}
\]

The equivalent expression is:
\[
\boxed{2(3x + 5)}
\]