Question

algebraic math problem
If 5a - 2b = b + 1 = 9, What is the value of a?

What i'v got so far is
5a -2b = b + 1 = 9
+ 2b + 2b
5a = 3b + 1 = 9
- 1 - 1
5a = 3b = 8

Answer 1

Am i doing this right?

Answer 2

This is an application of an axiom, which is also called "trasitive" property.
The axiom states that if a number "a" is equal to another number "b" but at the same time "b" is equal to a number "c", then "a" is equal to "c":
\[a=b=c\]
then:
\[a=c\]
\[b=c\]
That's a summarization of it, but hopefully you get the point.
so fo the problem:
\[5a-2b=b +1=9\]
we can view "5a-2b" as "a", "b+1" as "b" and "9" as "c", and it resonates with the structure of the trasitive axiom, so we can apply it:
\[5a-2b=9\]
\[b+1=9\]
So now you have two equations, where one is univarable, so take the second one, solve for "b" and replace it on the first equation.

Answer 3

Oh wow I did not know about that property, and sadly i have many to learn on this road however thanks so much! my work was:
background as you taught me
5a -2b = a
b+1 = b
9 = c
meaning two equations i have now 5a-2b=9 and b+1=9
and then to solve i took the univariable as suggested and was easier
b + 1 = 9
-1 -1
b = 8
therefore i used b to solve for the second equation
5a - 2b = 9
5a - 2(8) = 9
5a - 16 = 9
+16 +16
5a = 25
5a / 5 = 25 / 5
a = 5
Thank you once again :D

Answer 4

Very well done!