Question

Solve for the specified variable:
c(a+b)-d=f for a

Answer 1

`\large\boxed{a=(f+d)/(c)-b=(f+d-bc)/(c)}`

Explanation:

`c(a+b)-d=f\qquad\text{add}\ d\ \text{to both sides}\\\\c(a+b)=f+d\qquad\text{divide both sides by }\ c\\eq0\\\\a+b=(f+d)/(c)\qquad\text{subtract}\ b\ \text{from both sides}\\\\a=(f+d)/(c)-b\\\\a=(f+d)/(c)-(bc)/(c)\\\\a=(f+d-bc)/(c)`

Answer 2

a =
`(f+d)/(c)` - b

Explanation:

Given

c(a + b) - d = f ( add d to both sides )

c(a + b) = f + d ( divide both sides by the multiplier c )

a + b =
`(f+d)/(c)` ( subtract b from both sides )

a =
`(f+d)/(c)` - b