Question

How to solve the equation $5x - 1 = 3x + 5$?

Answer 1

Hint: Solve this equation $5x - 1 = 3x + 5$ by separating the variable terms on one side of the equation and the constant term on another side.
We use the addition-subtraction property to transform a given equation to an equivalent equation of the form x = a.
First, add $1$ to each side of the equation and then subtract $3x$ from each side of the equation.

Complete step-by-step answer:
We have to solve the equation $5x - 1 = 3x + 5$.
Basically, we have to find the value of $x$ .
Use the addition-subtraction property to transform a given equation to an equivalent equation of the form x = a
Add $1$ to the each side of the equation,
$5x - 1 + 1 = 3x + 5 + 1$
$ \Rightarrow 5x = 3x + 6$
Subtract $3x$ from each side of the equation.
$5x - 3x = 3x + 6 - 3x$
$ \Rightarrow 5x - 3x = 6$
$ \Rightarrow 2x = 6$
Divide $2$ to each side of the equation.
$ \Rightarrow \dfrac{{2x}}{2} = \dfrac{6}{2}$
$ \Rightarrow x = 3$

Final Answer: The solution of the equation $5x - 1 = 3x + 5$is $x = 3$.

Note:
 Substitute $x = 3$ into the equation the right-hand side of equation,
$5(3) - 1 = 15 - 1$
$5(3) - 1 = 14$
Substitute $x = 3$ into the equation the left-hand side of equation,
$3x + 5 = 3(3) + 5$
$3x + 5 = 14$
Since L.H.S. = R.H.S.
The solution of the equation is $x = 3$.