Question

How do you solve $4x+5=3x+8$?

Answer 1

Hint: In this problem we need to find the solution of the given equation i.e., we need to calculate the value of $x$ where the given equation is satisfied. For this we will apply the reverse arithmetic operations for the arithmetic operations which are present in the given equation. We can observe the term $3x$ is in addition on the right hand side. So, we will subtract the same term $3x$ on both sides of the given equation and we will simplify the equation by using known algebraic formulas. After that we can observe the term $5$ is in addition on the left hand side. So, we will subtract the same term $5$ on both sides of the equation and simplify the obtained equation to get the required solution.

Complete step by step answer:
Given equation $4x+5=3x+8$.
In the above equation we have $3x$ which is in addition on the right hand side. Hence subtracting the same term $3x$ on both sides of the above equation, then we will have
$\Rightarrow 4x+5-3x=3x+8-3x$
We know that $+a-a=0$. Applying this formula and simplifying the above equation, then we will have
$\Rightarrow x+5=8$
In the above equation we can observe that the term $5$ is in addition on the left hand side. Hence subtracting the same term $5$ on both sides of the above equation, then we will get
$\Rightarrow x+5-5=8-5$
Again, applying the formula $+a-a=0$ and simplifying the equation, then we will have
$\Rightarrow x=3$.
Hence the solution of the given equation $4x+5=3x+8$ is $x=3$.

Note:
We can also check whether the obtained solution is right or wrong by substituting the calculated value of $x$ in the given equation, then we will have
$\begin{align}
  & 4x+5=3x+8 \\
 & \Rightarrow 4\left( 3 \right)+5=3\left( 3 \right)+8 \\
 & \Rightarrow 12+5=9+8 \\
 & \Rightarrow 17=17 \\
\end{align}$
Hence our solution is correct.