To simplify the expression [tex]\((3x - 5) - (5x + 1)\)[/tex], follow these steps:
1. Distribute the negative sign across the second term in the expression:
[tex]\[
(3x - 5) - (5x + 1) \Rightarrow (3x - 5) - 5x - 1
\][/tex]
2. Rewrite the expression without parentheses:
[tex]\[
3x - 5 - 5x - 1
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x\)[/tex]-terms: [tex]\(3x - 5x\)[/tex]
- Combine the constants (numbers without [tex]\(x\)[/tex]): [tex]\(-5 - 1\)[/tex]
This gives:
[tex]\[
3x - 5x - 5 - 1 \Rightarrow (3x - 5x) + (-5 - 1)
\][/tex]
4. Simplify each part:
- For the [tex]\(x\)[/tex]-terms: [tex]\(3x - 5x = -2x\)[/tex]
- For the constants: [tex]\(-5 - 1 = -6\)[/tex]
Putting it all together, we get:
[tex]\[
-2x - 6
\][/tex]
Thus, the simplified expression is:
[tex]\[
-2x - 6
\][/tex]
