Solve the equation $\frac{x}{2}+1=\frac{1}{4}x-6$. Also check your solution

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

In $\frac{x}{2}+1=\frac{1}{4}x-6$, x is the variable which is the unknown quantity.

Constants: - In any expression or equation constant are the values which is fixed.

Here, 1 and 6 are constants.

Also, $\frac{x}{2}$ and $\frac{1}{4}x$ are the product of a constant and variable.

While performing addition in an equation, the same kind of elements or like terms are added together.

In the given equation, terms with the variable x will be added all together and while performing addition constant terms which are multiplied with the variables are added.

$\frac{x}{2}+1=\frac{1}{4}x-6$

Add $-\frac{1}{4}x-1$ both sides of the equation and simplify.

$\begin{array}{l}\frac{x}{2}+1-\frac{1}{4}x-1=\frac{1}{4}x-6-\frac{1}{4}x-1\\ \frac{x}{2}-\frac{1}{4}x+1-1=\frac{1}{4}x-\frac{1}{4}x-6-1\\ \frac{2x-x}{4}+0=0-6-1\\ \frac{x}{4}=-7\end{array}$

Multiply both the sides by 4 and simplify.

$\begin{array}{l}\frac{x}{4}\times 4=-7\times 4\\ x=-28\end{array}$

Hence on solving $\frac{x}{2}+1=\frac{1}{4}x-6$ the obtained value of x is $-28$.

Put $x=-28$ in $\frac{x}{2}+1=\frac{1}{4}x-6$ and check whether the value on the right-hand side is equal to the value on the left-hand side.

$\frac{\left(-28\right)}{2}+1=\frac{1}{4}\left(-28\right)-6$

First, evaluate the value on the left-hand side.

$\begin{array}{c}\frac{\left(-28\right)}{2}+1=\frac{-28+2\left(1\right)}{2}\\ =\frac{-28+2}{2}\\ =-\frac{26}{2}\\ =-13\end{array}$

Now, evaluate the values of right- hand side, that is, $\frac{1}{4}\left(-28\right)-6$.

$\begin{array}{c}\frac{1}{4}\left(-28\right)-6=\frac{-28-6\left(4\right)}{4}\\ =\frac{-28-24}{4}\\ =\frac{-52}{4}\\ =-13\end{array}$

Since the values of both sides are equal, the obtained result is true and verified.