To simplify the expression [tex]\((50) + (4x) - (xt) - 5(2x) + t\)[/tex], follow these detailed steps:
1. Distribute and rewrite each term:
- [tex]\(50\)[/tex]
- [tex]\(4x\)[/tex]
- [tex]\(-xt\)[/tex]
- [tex]\(-5(2x)\)[/tex]
- [tex]\(t\)[/tex]
2. Simplify the term [tex]\(-5(2x)\)[/tex] by distributing the [tex]\(-5\)[/tex]:
- [tex]\(-5(2x) = -10x\)[/tex]
3. Combine all terms:
- [tex]\(50 + 4x - xt - 10x + t\)[/tex]
4. Group like terms together:
- Constant terms: [tex]\(50\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(4x - 10x - xt\)[/tex]
- [tex]\(t\)[/tex] term: [tex]\(t\)[/tex]
5. Combine the like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(4x - 10x = -6x\)[/tex]
- Therefore, the expression in terms of [tex]\(x\)[/tex] and [tex]\(t\)[/tex] is [tex]\(-6x - xt\)[/tex]
6. Combine all the simplified terms together:
- Combining the constants and variables, you get: [tex]\(-6x - xt + t + 50\)[/tex]
Thus, the simplified form of the expression is:
[tex]\[
-tx + t - 6x + 50
\][/tex]
