Question

How do you simplify \[\dfrac{{2x + 5}}{2} = \dfrac{{3x - 2}}{6}\]?

Answer 1

Hint:In order to solve this question first, we write the equation as it is. And then we cross multiply the equation and then we separate the constant term and variable term on the opposite sides of the equal sign. Then we divide the coefficient of the variable with the constant term and find the final answer.


Complete step by step answer:
We have given an equation: \[\dfrac{{2x + 5}}{2} = \dfrac{{3x - 2}}{6}\]
We have to find the value of variable \[x\]
\[ \Rightarrow \dfrac{{2x + 5}}{2} = \dfrac{{3x - 2}}{6}\] (given)
Now we have to cross multiply the fractions to make it simple.
On cross multiplying-
\[ \Rightarrow 6\left( {2x + 5} \right) = 2\left( {3x - 2} \right)\]
On further multiplication the terms and expanding the terms.
\[ \Rightarrow 12x + 30 = 6x - 4\]
Now taking all the variable terms on one side and constant terms on another side.
\[ \Rightarrow 12x - 6x = - 30 - 4\]
Now on further calculating.
\[ \Rightarrow 6x = - 34\]
Here 6 is in multiplication so we take that to another side of equal to sign so that will go in divide.
\[ \Rightarrow x = \dfrac{{ - 34}}{6}\]
On dividing the terms.
\[ \Rightarrow x = \dfrac{{ - 34}}{6} \approx - 5.67\]
The value of \[x\] which satisfies the equation \[\dfrac{{2x + 5}}{2} = \dfrac{{3x - 2}}{6}\] is-
\[ \Rightarrow x = \dfrac{{ - 34}}{6} \approx - 5.67\]

Note: Although this question is very easy, to solve this type of question we have to always cross multiply the equation. To increase the difficulty level of the question they increase the power of the variable. It may be possible that we get a larger number of values of x which satisfies the equation.