Question

How do you solve \[\dfrac{x}{8} - \dfrac{1}{2} = 6\]

Answer 1

Hint: This problem is from an equation with one variable we can say. Here we have to find the value of x that is variable here. For that we will separate the constants on one side and variable x on the other side and then perform necessary mathematical operations like taking LCM, addition , multiplication and all we will find the value of x.

Complete step-by-step answer:
Given that,
 \[\dfrac{x}{8} - \dfrac{1}{2} = 6\]
Very first we will take that half term on RHS,
 \[ \Rightarrow \dfrac{x}{8} = 6 + \dfrac{1}{2}\]
See the sign of the term changes as it shifts on the other side of the equation. Now let’s take the LCM of the terms on RHS. So on cross multiplying we get,
 \[ \Rightarrow \dfrac{x}{8} = \dfrac{{6 \times 2 + 1 \times 1}}{2}\]
On adding terms in numerator,
 \[ \Rightarrow \dfrac{x}{8} = \dfrac{{13}}{2}\]
Now let’s move 8 from LHS to RHS so that variable x is totally separated.
 \[ \Rightarrow x = \dfrac{{13}}{2} \times 8\]
8 was in the denominator on LHS so it is now in the numerator on RHS. So now divide 8 by 2 we get,
 \[ \Rightarrow x = 13 \times 4\]
Now just multiply the numbers,
 \[ \Rightarrow x = 52\]
This is the value of x.
So, the correct answer is “ x = 52”.

Note: Here we cannot directly find the value of x until it is separated from constants. Note that the number of variables is equal to the number of equations. Here only one variable is there so one equation is sufficient to solve. Here also if we come across fractions as the answer, simplify it to the simplest form. Variables are generally the alphabets of English. Variables are not having fixed values, that is their values always change but constants have fixed values.