To find the value of [tex]\( a \)[/tex] in the equation [tex]\( 5a - 10b = 45 \)[/tex] when [tex]\( b = 3 \)[/tex], follow these steps:
1. Substitute [tex]\( b = 3 \)[/tex] into the equation:
[tex]\[
5a - 10(3) = 45
\][/tex]
2. Simplify the equation by multiplying and combining like terms:
[tex]\[
5a - 30 = 45
\][/tex]
3. To isolate [tex]\( a \)[/tex], add 30 to both sides of the equation:
[tex]\[
5a - 30 + 30 = 45 + 30
\][/tex]
[tex]\[
5a = 75
\][/tex]
4. Finally, solve for [tex]\( a \)[/tex] by dividing both sides of the equation by 5:
[tex]\[
a = \frac{75}{5}
\][/tex]
[tex]\[
a = 15
\][/tex]
Thus, the value of [tex]\( a \)[/tex] is [tex]\(\boxed{15}\)[/tex].
