To solve the equation [tex]\(M = 7a + 5ab\)[/tex] for [tex]\(a\)[/tex], follow these detailed steps:
1. Start with the given equation:
[tex]\[
M = 7a + 5ab
\][/tex]
2. Factor [tex]\(a\)[/tex] out of the right-hand side of the equation:
[tex]\[
M = a(7 + 5b)
\][/tex]
3. Isolate [tex]\(a\)[/tex] by dividing both sides of the equation by [tex]\((7 + 5b)\)[/tex]:
[tex]\[
a = \frac{M}{7 + 5b}
\][/tex]
Now let's match the solution against the provided multiple-choice options:
- Option a: [tex]\( \frac{M}{7 - 5b} \)[/tex]
- Option b: [tex]\( M(7 + 5b) \)[/tex]
- Option c: [tex]\( \frac{M}{7 + 5b} \)[/tex]
- Option d: [tex]\( M(7 - 5b) \)[/tex]
The correct solution is [tex]\( a = \frac{M}{7 + 5b} \)[/tex], which corresponds to option (c).
Therefore, the correct answer is:
[tex]\[
(c) \frac{M}{7 + 5b}
\][/tex]
