Question

How do you solve $\dfrac{3x}{4}+2=4x-1$ ?

Answer 1

Hint: Problems related to solving this type of linear equations can be easily solved by just doing simple rearrangements and simplifications. We take all the terms related to $x$ on one side of the equation and take the other constant terms to the other side of the equation. Then, doing some simplifications we will get the solution of the given problem.

Complete step-by-step answer:
The equation we have is
$\dfrac{3x}{4}+2=4x-1$
For solving this equation, we must separate the terms related to $x$ and the other constant terms which do not contain $x$ .
So, we move all the terms which contain $x$ to the left-side of the equation by subtracting $4x$ from both the sides of the equation as shown below
$\Rightarrow \dfrac{3x}{4}+2-4x=-1$
Also, we move all the constant terms that do not contain $x$ to the right-hand side of the equation by subtracting $2$ from both the sides of the equation as shown below

$\Rightarrow \dfrac{3x}{4}-4x=-1-2$
If we take the negative sign from both the right- and left-hand side of the above equation we can rewrite the above equation as
$\Rightarrow 4x-\dfrac{3x}{4}=1+2$
Subtracting $\dfrac{3x}{4}$ from $4x$ in the above equation we get
$\Rightarrow \dfrac{13x}{4}=1+2$
Adding the like terms in the right-hand side of the above equation we get
$\Rightarrow \dfrac{13x}{4}=3$
Multiplying both sides of the above equation with $4$ we get
$\Rightarrow 13x=12$
Dividing both the sides of the above equation by $13$ we get
$\Rightarrow x=\dfrac{12}{13}$
Therefore, the solution of the given equation is $x=\dfrac{12}{13}$ .

Note: We must be careful while moving the terms to one side from another to avoid mistakes. Also, we must consider the signs of the numbers properly so that summation and subtraction become flawless. We can also take the two sides of the given equation to be two separate equations. Plotting them on a graph paper and finding out the point of intersection will give us the solution.