Question

Find the value of x. If $\dfrac{3x+5}{5}-\dfrac{5x-7}{6}=\dfrac{x-2}{3}$

Answer 1

Hint: Remember the basic concept of operations on fractions. We need to remember the Least Common Multiple. After simplifying we will get the value of x.

Complete step by step answer:
The given equation is : $\dfrac{3x+5}{5}-\dfrac{5x-7}{6}=\dfrac{x-2}{3}$
As we observe denominators of all the terms are different, we cannot solve the terms directly.
So firstly, we need to multiply each term with such a number that denominators become equal.
For the denominators to be equal, we multiply each term with the least common multiple of the denominators. If the denominators have no common multiple, the product of the denominators is the least common multiple and hence we multiply each term with the product of the denominators. But remember this is only when there is no common multiple of the denominators.
Tackling the left hand side first, we multiply each term with the Least Common Multiple of 6 and 5.
Least common multiple, also known as LCM of 6 and 5 is 30.
On multiplying the left hand side of the given equation by 30, we get
$\dfrac{6\left( 3x+5 \right)-5\left( 5x-7 \right)}{5\times 6}=\dfrac{x-2}{3}$
On solving further, we get
$\dfrac{\left( 18x+30 \right)-\left( 25x-35 \right)}{2}=\dfrac{x-2}{3}$
$\dfrac{18x+30-25x+35}{30}=\dfrac{x-2}{3}$
$\dfrac{65-7x}{30}=\dfrac{x-2}{3}$
Equating the two sides to find the value of x:
$3\left( 65-7x \right)=30\left( x-2 \right)$
$195-21x=30x-60$
Bring all terms related to x on one side and all the constant terms on the other side.
Now we get,
$30x+21x=195+60$
$51x=255$
Finally the value of x is,
$x=\dfrac{255}{51}=5$
Hence $x=5$

Note: Simplify so that all constant terms come on one side and all the terms related to x on one side. Mistakes are usually made in the term used for multiplication. Make sure to find the correct LCM.