Question

Solve $5y - 2\left[ {y - 3\left( {y - 5} \right)} \right] = 6$

Answer 1

Hint: In the above question we have to find the value of the variable $y$ . We are having the left side of the equation as a combination of algebraic operations that is addition , subtraction, brackets .
So we apply the concept of BODMAS and we will also solve brackets using the hierarchy of solving brackets .

Formula used: We need to solve the given question BODMAS where $B$ is Bracket, O stands for multiplication, D is for Division, M stands for Multiplication, A is for Addition, S for Subtraction.
For solving brackets , first of all bar \[\overline {} \] bracket is solved , after that parenthesis bracket is solved $()$ ,
Then we solve for the square $[]$ bracket . The last curly bracket is solved $\{ \} $.

Complete step-by-step solution:
 In this question to find out the value of variable $y$ we will start solving from the left hand side of the given equation .
We first need to simplify the brackets
$ \Rightarrow $$5y - 2\left[ {y - 3\left( {y - 5} \right)} \right] = 6$
Firstly we will solve , parenthesis bracket which is $3(y - 5)$
So we get ,
$ \Rightarrow $$5y - 2\left[ {y - 3y - 15} \right] = 6$
Now we will solve for next bracket that is square bracket $2\left[ {y - 3y + 5} \right]$
Again simplifying the square bracket
$ \Rightarrow $ $5y - 2y + 6y - 30 = 6$
Applying addition as per BODMAS rule doing addition first
$ \Rightarrow $ $11y - 2y - 30 = 6$
Now performing subtraction
$ \Rightarrow $ $9y - 30 = 6$
Taking variable in Left hand side and constant which is number in right side.
$ \Rightarrow $ $9y = 6 + 30$
We get
$ \Rightarrow $ $9y = 36$
Simplifying the above we get
$\Rightarrow$$y = 4$

So, the required result is $y = 4$.

Note: Students can commit a big error if they don’t know about the basic algebraic concepts and BODMAS.
Another concept which is used is PEMDAS
P – parenthesis bracket ()
E- exponents
M- multiplication
D- division
A-addition
S - subtraction
Another thing is To solve such type of solution we need to remember the sign rule:
$ + \times - = - $
$ - \times - = + $
$ + \times + = + $