Question

How do you solve $2x-\dfrac{5}{9}=\dfrac{7x+8}{9}$ ?

Answer 1

Hint: First take the l.c.m as ‘9’ on the left hand side of the equation and cancel out 9 from both the sides. Then separate the variable ‘x’ and constants on the different sides of the equation. Do the necessary calculations and solve for ‘x’ to get the required solution.

Complete step-by-step solution:
Solving the equation means we have to find the value of ‘x’ for which the equation gets satisfied.
Considering the given equation $2x-\dfrac{5}{9}=\dfrac{7x+8}{9}$
Taking the l.c.m. as ‘9’ on the left hand side of the equation, we get
$\begin{align}
  & \Rightarrow \dfrac{2x\cdot 9-5}{9}=\dfrac{7x+8}{9} \\
 & \Rightarrow \dfrac{18x-5}{9}=\dfrac{7x+8}{9} \\
\end{align}$
Multiplying by ‘9’ on both the sides we get
$\Rightarrow \dfrac{9\left( 18x-5 \right)}{9}=\dfrac{9\left( 7x+8 \right)}{9}$
Cancelling out ‘9’ both from the numerator and the denominator from both the sides, we get
$\Rightarrow 18x-5=7x+8$
Now we have to separate the variable and constants.
Bringing all ‘x’ terms to right hand side and all constants to left hand side of the equation, we get
 $\begin{align}
  & \Rightarrow 18x-7x=8+5 \\
 & \Rightarrow 11x=13 \\
\end{align}$
Dividing both sides by 11, we get
$\Rightarrow \dfrac{11x}{11}=\dfrac{13}{11}$
Cancelling out 11 both from the numerator and the denominator on the left hand side, we get
$\Rightarrow x=\dfrac{13}{11}$
This is the required solution of the given question.

Note: Taking l.c.m. of 9 on the left side of the equation should be the first approach to solve this question. Division part should be eliminated by multiplying ‘9’ on both sides. Necessary calculations should be done to get the value of ‘x’ as per the requirement of the question.