Question

Find x..
\[\dfrac{2x+7}{5}-\dfrac{3x+11}{2}=\dfrac{2x+8}{3}-5\]

Answer 1

Hint: To find x, first simplify the given equation. Rules of BODMAS are to be used while simplifying. Find LCM to subtract fractions. Use the cross product rule for further simplification. Then, group the like terms together.

Complete step-by-step answer:
The value of x is calculated as:
     \[\begin{align}
  & \text{ }\dfrac{2x+7}{5}-\dfrac{3x+11}{2}=\dfrac{2x+8}{3}-\dfrac{5}{1} \\
 & \Rightarrow \dfrac{2\left( 2x+7 \right)-5\left( 3x+11 \right)}{10}=\dfrac{1\left( 2x+8 \right)-3\left( 5 \right)}{3} \\
 & \Rightarrow \dfrac{4x+14-15x-55}{10}=\dfrac{2x+8-15}{3} \\
 & \Rightarrow \dfrac{-11x-41}{10}=\dfrac{2x-7}{3} \\
 & \Rightarrow 3\left( -11x-41 \right)=10\left( 2x-7 \right) \\
 & \Rightarrow -33x-123=20x-70 \\
 & \Rightarrow -123+70=20x+33x \\
 & \Rightarrow 53x=-53 \\
 & \Rightarrow x=\dfrac{-53}{53} \\
 & \Rightarrow x=-1 \\
\end{align}\]

Note: To check whether the solution of x is correct or not, substitute the calculated value of x in the original equation and verify if both sides of the equation are equal. On substituting -1 for x, in the original equation and simplifying the expressions, -3 is obtained on both sides. Since, the expression on both sides of the equation is equal, the value of x is verified. LCM is calculated using prime factorization or division method. Distributive property is used for multiplication. While multiplication, the signs of the numbers should be written carefully. Addition and subtraction of integers should be known thoroughly. If the numbers are of different signs, then they are subtracted and the sign of the greater number is assigned to the result. If both numbers are of the same sign, they are added and a sign of the numbers is assigned to the result. Also, it is important to keep in mind that the sign of a number changes when transferred to the other side. To group the like terms together, -33x is transferred to the other side of the equation, hence it becomes +33x. Similarly, -70 becomes 70.