To rewrite the expression [tex]\((9x + 5) + (5x + 9)\)[/tex] in its simplest form, follow these steps:
1. Combine like terms within the parentheses:
- The expression is originally written as [tex]\((9x + 5) + (5x + 9)\)[/tex].
2. Group the [tex]\(x\)[/tex] terms together and the constant terms together:
- Identify the terms with [tex]\(x\)[/tex]: [tex]\(9x\)[/tex] and [tex]\(5x\)[/tex].
- Identify the constant terms: 5 and 9.
3. Add the coefficients of the [tex]\(x\)[/tex] terms:
- [tex]\(9x + 5x\)[/tex]: Combine the coefficients (9 and 5) which gives [tex]\(14x\)[/tex].
4. Add the constant terms:
- [tex]\(5 + 9\)[/tex]: Add the constants which gives 14.
5. Combine the results:
- The simplified expression is the sum of the combined [tex]\(x\)[/tex] terms and the combined constant terms, which is [tex]\(14x\)[/tex] and 14 respectively.
Putting it all together, the simplified form of [tex]\((9x + 5) + (5x + 9)\)[/tex] is:
[tex]\[ 14x + 14 \][/tex]
So, the simplified expression is [tex]\(14x + 14\)[/tex].
