Certainly! Let's solve the equation [tex]\(5a - 2b = 15\)[/tex] for [tex]\(a\)[/tex] step-by-step.
### Step-by-Step Solution:
1. Start with the given equation:
[tex]\[
5a - 2b = 15
\][/tex]
2. Isolate the term involving [tex]\(a\)[/tex]:
To isolate [tex]\(5a\)[/tex], add [tex]\(2b\)[/tex] to both sides of the equation:
[tex]\[
5a - 2b + 2b = 15 + 2b
\][/tex]
Simplifying this, we get:
[tex]\[
5a = 15 + 2b
\][/tex]
3. Solve for [tex]\(a\)[/tex]:
To solve for [tex]\(a\)[/tex], we need to divide both sides of the equation by 5:
[tex]\[
a = \frac{15 + 2b}{5}
\][/tex]
4. Simplify the expression:
Split the fraction into two separate fractions to simplify:
[tex]\[
a = \frac{15}{5} + \frac{2b}{5}
\][/tex]
5. Calculate the division:
Evaluate the fractions individually:
[tex]\[
\frac{15}{5} = 3 \quad \text{and} \quad \frac{2b}{5} = \frac{2}{5}b
\][/tex]
6. Combine the results:
Finally, combine the terms to express [tex]\(a\)[/tex]:
[tex]\[
a = 3 + \frac{2}{5}b
\][/tex]
So, the solution to the equation [tex]\(5a - 2b = 15\)[/tex] for [tex]\(a\)[/tex] is:
[tex]\[
a = \frac{2b}{5} + 3
\][/tex]
This is the simplified form of [tex]\(a\)[/tex] in terms of [tex]\(b\)[/tex].
