Question

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

Answer 1

Hint: To solve \[\dfrac{x+1}{3}=\dfrac{2x-1}{4}\], we need to multiply the given equation with 12 on both the sides of the equation. And the denominator of the equation gets cancelled in both the left and right side of the equation. Then, make necessary calculations to bring all the ‘x’ terms to the left-hand side of the equation and the constants to the right-hand side of the equation. Then, divide the whole obtained equation by -2. And we get the value of ‘x’ which is the required solution.

Complete step by step answer:
According to the question, we are asked to solve \[\dfrac{x+1}{3}=\dfrac{2x-1}{4}\].
We have been given the equation is \[\dfrac{x+1}{3}=\dfrac{2x-1}{4}\] --------(1)
First, let us consider the equation (1).
We have to multiply both the sides of the equation by 12.
We get,
\[\Rightarrow 12\times \dfrac{x+1}{3}=\dfrac{2x-1}{4}\times 12\]
On further simplifications, we get,
\[\Rightarrow \left( 4\times 3 \right)\dfrac{x+1}{3}=\dfrac{2x-1}{4}\left( 4\times 3 \right)\]
Cancelling the common terms, that is, 3 in the left-hand side and 4 in the right-hand side of the equation, we get,
\[4\left( x+1 \right)=3\left( 2x-1 \right)\]
Using distributive property, that is, \[a\left( b+c \right)=ab+ac\]
We get,
\[4x+4=3\left( 2x \right)-3\]
\[\Rightarrow 4x+4=6x-3\] ------(2)
Now subtract 6x from both the sides of the equation (2).
\[\Rightarrow 4x+4-6x=6x-6x-3\]
We know that terms with opposite signs and same magnitude cancel out.
Therefore, we get,
\[\Rightarrow -2x+4=-3\] --------(3)
Then, add -4 on both the sides of the equation (3).
\[\Rightarrow -2x+4-4=-3-4\]
On further simplification, we get,
\[\Rightarrow -2x=-7\]
Divide -2 on both the sides of the obtained equation.
\[\Rightarrow \dfrac{-2x}{-2}=\dfrac{-7}{-2}\]
\[\therefore x=\dfrac{7}{2}\]
Hence, from the above, the value of x is \[\dfrac{7}{2}\].

Note:
We can also solve this question by cross multiplying the given equation.
Therefore, we get \[4\left( x+1 \right)=3\left( 2x-1 \right)\]. Then, follow the above steps. Then, make necessary calculations and find the value of x as obtained in the above solution. We should not make calculation mistakes based on sign conventions.