To determine the value of [tex]\( a \)[/tex] in the equation [tex]\( 5a - 10b = 45 \)[/tex] given that [tex]\( b = 3 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
5a - 10b = 45
\][/tex]
2. Substitute the given value of [tex]\( b = 3 \)[/tex] into the equation:
[tex]\[
5a - 10 \times 3 = 45
\][/tex]
3. Simplify the equation by performing the multiplication:
[tex]\[
5a - 30 = 45
\][/tex]
4. To isolate [tex]\( a \)[/tex], add 30 to both sides of the equation:
[tex]\[
5a - 30 + 30 = 45 + 30
\][/tex]
This simplifies to:
[tex]\[
5a = 75
\][/tex]
5. Finally, divide both sides by 5 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{75}{5}
\][/tex]
[tex]\[
a = 15
\][/tex]
Thus, the value of [tex]\( a \)[/tex] is [tex]\( \boxed{15} \)[/tex].
