QUESTION

# Find the value of $y$of the given below equation:$15\left( {y - 4} \right) - 2\left( {y - 9} \right) + 5\left( {y + 6} \right) = 0$

Hint: First of all, identify the variable in the given equation. As it is a linear equation in one variable, we need to solve for this variable using simple math applications. So, use this concept to reach the solution of the given problem.

Complete step-by-step solution -
Given that $15\left( {y - 4} \right) - 2\left( {y - 9} \right) + 5\left( {y + 6} \right) = 0$
Now, we need to solve the given equation in the simplest form in order to find the value of $y$.
Multiplying with the coefficients before the brackets, we get
$\Rightarrow 15y - 15 \times 4 - 2y - 2 \times \left( { - 9} \right) + 5y + 5 \times 6 = 0 \\ \Rightarrow 15y - 60 - 2y + 18 + 5y + 30 = 0 \\$
Grouping the common terms, we get
$\Rightarrow \left( {15y - 2y + 5y} \right) + \left( { - 60 + 18 + 30} \right) = 0 \\ \Rightarrow 18y - 12 = 0 \\ \Rightarrow 18y = 12 \\$
Dividing both sides with 18 we get
$\Rightarrow \dfrac{{18y}}{{18}} = \dfrac{{12}}{{18}} \\ \Rightarrow y = \dfrac{{12}}{{18}} = \dfrac{2}{3} \\ \therefore y = \dfrac{2}{3} \\$
Thus, $y = \dfrac{2}{3}$ satisfies the equation $15\left( {y - 4} \right) - 2\left( {y - 9} \right) + 5\left( {y + 6} \right) = 0$.

Note: The obtained variable value must satisfy the given equation if we put the value in that equation, then only the obtained answer is correct. Here we have used simple math applications like addition, subtraction, multiplication and division.