Question

How do you solve $7x - 4 + x = 12$?

Answer 1

Hint: First step is to add variables terms together given in the left hand side of the equation. Next step is to isolate the variable terms on one side, and the constant terms on the other side by performing the same mathematical operations on both sides of the equation. Next step is to make the coefficient of the variable equal to $1$ using multiplication or division property.

Complete step by step answer:
The algebraic equation is $7x - 4 + x = 12$.
We have to find the value of $x$.
First we have to add variable terms together given in the left hand side of the equation.
So, adding $7x$ and $x$ in the given equation.
$ \Rightarrow 8x - 4 = 12$
Next step is to isolate the variable terms on one side, and the constant terms on the other side by performing the same mathematical operations on both sides of the equation.
So, adding $4$ to both sides of the equation $8x - 4 = 12$.
$ \Rightarrow 8x - 4 + 4 = 12 + 4$
It can be written as
$ \Rightarrow 8x = 16$
Next step is to make the coefficient of the variable equal to $1$ using multiplication or division property.
So, dividing both sides of the equation $8x = 16$ by $8$.
$ \Rightarrow \dfrac{{8x}}{8} = \dfrac{{16}}{8}$
It can be written as
$ \Rightarrow x = 2$

Therefore, $x = 2$ is the solution of $7x - 4 + x = 12$.

Note: An algebraic equation is an equation involving variables. It has an equality sign. The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS).

In an equation the values of the expressions on the LHS and RHS are equal. This happens to be true only for certain values of the variable. These values are the solutions of the equation.
How to find the solution of an equation?
We assume that the two sides of the equation are balanced. We perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed.
Solving Equations having the Variable on both sides:
Transpose variable term to LHS.
Transpose constant term on RHS.
Then it will become the algebraic equation. It can be solved as explained above.