Sure, let's simplify the expression [tex]\((3x - 5) + (5x + 1)\)[/tex] step-by-step.
1. Distribute and combine like terms:
- Start by identifying and combining the like terms from each parentheses.
- The given expression is [tex]\((3x - 5) + (5x + 1)\)[/tex].
- First, combine the [tex]\(x\)[/tex] terms:
[tex]\[
3x + 5x = 8x
\][/tex]
- Next, combine the constant terms:
[tex]\[
-5 + 1 = -4
\][/tex]
2. Put the combined terms together:
- Now, combine these results to get the simplified expression:
[tex]\[
8x - 4
\][/tex]
So, the simplified form of the expression [tex]\((3x - 5) + (5x + 1)\)[/tex] is [tex]\(8x - 4\)[/tex].
Now, let's check the given options to see which one matches our simplified expression:
- Option 1: [tex]\(8x - 6\)[/tex]
- Option 2: [tex]\(8x + 4\)[/tex]
- Option 3: [tex]\(8x - 4\)[/tex]
- Option 4: [tex]\(2x - 4\)[/tex]
The correct option, matching our simplified expression [tex]\(8x - 4\)[/tex], is:
[tex]\[
\boxed{8x - 4}
\][/tex]
