x/5 - x = 1/2

To solve the equation.

Solution:

x/5 - x = 1/2..... (1) is a linear equation of one variable x.

We solve the linear equation of one variable by operations adding or subtracting equals. Or by multiplying or dividing by equals ( bur no multiplication or division by zero) and finally arriving at the value of the variable.

Mutiply the equation by the LCM 10 of denominators, 5 and 2. The denominators get rid off.

10(x/5) -10x = 10(1/2)

Simplify.

2x-10x = 5

Simplify.

-8x = 5

Divide by -8.

-8x/-8 = 5/-8

Simplify.

x = -5/8

Tally; Put x = -5/8 in the given equation: x/5-x = 1/2.

LHS = (-5/8)/5 - (-5/8) = -1/8+5/8 = (5-1)/8 = 4/8 = 1/2= RHS.

The equation x/5-x=1/2 can be solved as follows:

First we make the denominator of all the terms the same or let's make it 5*2=10.

We get x/5-x=1/2

=> (2*x)/(2*5)- 10*x/10 =(5*1)/(2*5)

=> 2x/10-10x/10=5/10

cancelling the denominator as it is the same for all the terms

=>2x-10x=5

=>-8x=5

=>x=5/(-8)

**or x=(-5/8)**