To simplify the given algebraic expression [tex]\(15x - 10a - 18xb - 12b\)[/tex], follow these detailed steps:
1. Identify and Group Like Terms:
- The terms involving [tex]\(x\)[/tex]: [tex]\(15x\)[/tex] and [tex]\(-18xb\)[/tex].
- The terms not involving [tex]\(x\)[/tex]: [tex]\(-10a\)[/tex] and [tex]\(-12b\)[/tex].
2. Combine Like Terms:
- For the terms involving [tex]\(x\)[/tex]:
[tex]\[
15x - 18xb
\][/tex]
- Since there are no like terms further simplifying [tex]\(15x - 18xb\)[/tex] and [tex]\(-10a\)[/tex] and [tex]\(-12b\)[/tex], you'll leave them as they are.
3. Construct Simplified Expression:
- Combine the results from the grouped terms:
[tex]\[
15x - 18xb - 10a - 12b
\][/tex]
Since no further simplification or factorization can condense this expression any further, the simplified form of the expression is:
[tex]\[
-10a - 18bx - 12b + 15x
\][/tex]
Thus, the original expression [tex]\(15x - 10a - 18xb - 12b\)[/tex] simplifies to:
[tex]\[
-10a - 18bx - 12b + 15x
\][/tex]
