William Collins

2022-01-04

Solve the equation for x. $fx-gx=h$

lovagwb

Step 1
We need to solve the equation for the variable x, which means that we need to isolate the variable x on one side of the equation.
We can solve an equation by applying inverse operations to the equation, where subtraction is the inverse of addition and division is the inverse of multiplication.
Moreover, the inverse operation needs to be applied to both sides of the equation. That is, if we change one side of the equation, then the other side of the equation needs to be changed in the same manner if we want to keep the equation balanced.
Step 2
Solve equation
$fx-gx=h$
Use distributive property $\left(a-b\right)c=a\cdot b-a\cdot c$
$\left(f-g\right)x=h$
Step 3
We need to undo the multiplication, which is done by dividing both sides of the equation by the same expression:
$\frac{\left(f-g\right)x}{\left(f-g\right)}=\frac{h}{\left(f-g\right)}$
Simplify both sides of the equation:
$x=\frac{h}{f-g}$

limacarp4

$fx-gx=h$
Taking x common on LHS,
$x\left(f-g\right)=h$
$x=\frac{h}{f-g}$
$\therefore x=\frac{h}{f-g}$

karton

$Fx-gx=h\phantom{\rule{0ex}{0ex}}\frac{Fx}{f}-\frac{gx}{g}=\frac{h}{fg}\phantom{\rule{0ex}{0ex}}x-x=\frac{h}{fg}\phantom{\rule{0ex}{0ex}}x=\frac{h}{fg}$