Question

Find the value of \[x\],\[\dfrac{4x}{5}-2=\dfrac{6x}{15}\]

Answer 1

Hint: In this question, first we need to write down the equation, then equate the denominator to have a common denominator to further solve it. After using different operations such as multiplication, addition, division and subtraction find the value of $ x $ .

Complete step-by-step answer:
We will have to solve the following equation in a number of steps.
Let us first write down the equation,
\[\dfrac{4x}{5}-2=\dfrac{6x}{15}\]
Now, we shall multiply and divide the number - 2 by 5 to have a common denominator on the Left-hand side of the equation.
\[\dfrac{4x-10}{5}=\dfrac{6x}{15}\]
Multiply by 15 on both the sides of the equation, we get
\[12x-30=6x\]
Now, add the number 30 on both the sides of the equation, we get
\[\begin{align}
  & 12x-30+30=6x+30 \\
 & 12x=6x+30
\end{align}\]
After this, we will subtract $ 6x $ on both the sides of the equation to get
\[\begin{align}
  & 12x-6x=6x-6x+30 \\
 & 6x=30
\end{align}\]
Let us find the value of $ x $ by dividing both the sides by 6, we get
\[\begin{align}
  & x=\dfrac{30}{6} \\
 & =5
\end{align}\]

Note: The following type of question deals with linear equations. Since only one variable (\[x\]) is to be found, only one equation \[\dfrac{4x}{5}-2=\dfrac{6x}{15}\] is required. It is solved by equating the L.H.S to the R.H.S and further equating the constant value to the variable. This type of equation with one variable with the power of 1 to the determining variable is also known as monomial. We can also solve by making the denominators on both the left-hand side and the right-hand side of the equation common.