Given
a) 2p+5r=q
b) x/5-g=a
c) a/b=c
Find
An expression for ...
a) p
b) x
c) b
Solution
In general, you "undo" what was done to the variable. You do that in the reverse of the order in which it was done.
a) The variable is multiplied by 2 and 5r is added. We add the opposite of 5r and multiply by the reciprocal of 2.
[tex]2p+5r=q\\2p=q-5r\\\\p=\dfrac{q-5r}{2}[/tex]
b) The variable is multiplied by 1/5 and g is subtracted. We add g and multiply by 5.
[tex]\dfrac{x}{5}-g=a\\\dfrac{x}{5}=a+g\\\\x=5(a+g)[/tex]
c) The reciprocal of b is computed, then multiplied by a. We divide by a, then take the reciprocal.
[tex]\dfrac{a}{b}=c\\\dfrac{1}{b}=\dfrac{c}{a}\\\\b=\dfrac{a}{c}[/tex]
