Question

Solve the given equation for x:
$\dfrac{7}{3x+4}=\dfrac{7}{6x-2}$
(a)-2
(b) -1
(c) 0
(d) 2

Answer 1

Hint: Here, we will first do cross multiplication, after that we will take all the terms containing the variable x to one side and the constant terms to the other side. Then, we will obtain the value of x.

Complete step-by-step answer:
We know that a linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form $ax+b=0$, where x is the variable, ‘a’ and ‘b’ are real numbers and are not equal to zero.
 The steps for solving a linear equation in one variable are as follows:
In the first step, transfer all the variables on one side of the equation, that is transfer variables on one side of the equation and constants on the other side.
Then in the next step we get the value of the variable by solving.
Here, we are given $\dfrac{7}{3x+4}=\dfrac{7}{6x-2}$
On cross multiplication, we get:
$7\left( 6x-2 \right)=7\left( 3x+4 \right)$
$\Rightarrow 42x-14=21x+28$
Now, on separating the variables on left hand side and constants on right hand side, we get:
$\begin{align}
  & 42x-21x=28-\left( -14 \right) \\
 & \Rightarrow 21x=42 \\
 & \Rightarrow x=2 \\
\end{align}$
Hence, option (d) is the correct answer.

Note: Students should note here that whenever a term is transferred from one side of an equation to the other side its sign gets reversed. The calculations must be done properly to avoid mistakes.