Solve the equation $5a+2=6-7a$. 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 $5a+2=6-7a$, a is the variable which is the unknown quantity.

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

Here, 2 and 6 are constants.

Also, $5a$ and $7a$ 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 a will be added all together and while performing addition constant terms which are multiplied with the variables are added.

$5a+2=6-7a$

Add $7a-2$ both sides of the equation and simplify.

$\begin{array}{l}5a+2+7a-2=6-7a+7a-2\\ 5a+7a+2-2=6-2\\ 12a=4\end{array}$

Multiply both sides by $\frac{1}{12}$ and simplify.

$\begin{array}{l}\frac{1}{12}\times 12a=\frac{1}{12}\times 4\\ a=\frac{1}{3}\end{array}$

Hence on solving $5a+2=6-7a$ the obtained value of a is $\frac{1}{3}$.

Put $a=\frac{1}{3}$in$5a+2=6-7a$ and check whether the value on the right-hand side is equal to the value on the left-hand side.

$5\left(\frac{1}{3}\right)+2=6-7\left(\frac{1}{3}\right)$

First, evaluate the value at left- hand side.

$\begin{array}{c}5\left(\frac{1}{3}\right)+2=\frac{5}{3}+2\\ =\frac{5+3\left(2\right)}{3}\\ =\frac{5+6}{3}\\ =\frac{11}{3}\end{array}$

Now evaluate the values of right- hand side, that is, $6-7\left(\frac{1}{3}\right)$.

$\begin{array}{c}6-7\left(\frac{1}{3}\right)=6-\frac{7}{3}\\ =\frac{3\left(6\right)-7}{3}\\ =\frac{18-7}{3}\\ =\frac{11}{3}\end{array}$

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