Question

How do you solve $5x - 3 = 13 - 3x?$

Answer 1

Hint:Eliminate the term which is the coefficient of “x” in the right hand side (R.H.S) and also eliminate the constant from left hand side (L.H.S) by doing addition with their respective additive inverse to the both sides. Finally you will get an equation in which the left hand side will consist only of the term which is the coefficient of “x” and the right hand side will consist of only constant, then divide both sides with the coefficient of “x”.

Complete step by step solution:
In order to solve $5x - 3 = 13 - 3x,$ we need to go through some steps to eliminate the term which is the coefficient of “x” in the right hand side and the constant from the left hand side. We will start by eliminating $ - 3$ in the L.H.S. of the given equation by adding $3$ to both sides.

We are adding $3$ because it is the additive inverse of $ - 3$ and adding to both sides because only then it will not affect the real equation and maintain the respective balance of the equation.

First rearranging the equation and then adding $3$ both sides, we will get
$
\Rightarrow 5x - 3 = 13 - 3x \\

\Rightarrow 5x - 3 = - 3x + 13 \\

\Rightarrow 5x - 3 + 3 = - 3x + 13 + 3 \\
$
Solving further,
$
\Rightarrow 5x - 0 = - 3x + 16 \\

\Rightarrow 5x = - 3x + 16 \\
$
Now, adding $3x$ to both sides in order to eliminate $ - 3x$, we will get
$
\Rightarrow 5x = - 3x + 16 \\

\Rightarrow 5x + 3x = - 3x + 16 + 3x \\

\Rightarrow 5x + 3x = - 3x + 3x + 16 \\

\Rightarrow 8x = 0 + 16 \\

\Rightarrow 8x = 16 \\
$
Now dividing both sides with $8$, which is the coefficient of “x”, we will get
\[
\Rightarrow 8x = 16 \\

\Rightarrow \dfrac{{8x}}{8} = \dfrac{{16}}{8} \\

\Rightarrow x = 2 \\
\]
$\therefore $ we get the required solution for the equation $5x - 3 = 13 - 3x$ which is $x = 2$

Note: If $b$ is the additive inverse of $a$ , then the sum of $a\;{\text{and}}\;b$ will be equals to $0$ $ \Rightarrow a + b = 0$ then the value $b$ will be given as $ \Rightarrow b = 0 - a = - a$. There also exists multiplicative inverses, if $a$ is the number then its multiplicative inverse (say $b$) will be given as $b = \dfrac{1}{a}$