Question

How do you simply $ 7-4[3-(4y-5)] $?

Answer 1

Hint: In this question, we have to simplify an equation that consists of a single variable. Therefore, this equation is an algebraic equation, so we will apply the simple BODMAS method, to simplify our problem. This method implies Brackets Of Division, Multiplication, Addition, and Subtraction. In this method, we open the brackets and then solve for division, multiplication, addition, and then subtraction. For solving this problem, we first solve the brackets of the equation, and then we will apply distributive property $ a(b+c+d)=ab+ac+ad $ in the equation. After necessary calculations, we see that all brackets and multiplications are done successfully, then we will do addition and after that subtraction, to get a simplified answer for the equation.

Complete step by step answer:
According to the question, we have to simplify the algebraic equation $ 7-4[3-(4y-5)] $.
So, we will use the BODMAS method to get the required solution.
Equation : $ 7-4[3-(4y-5)] $ -------- (1)
Now, let us first solve for the brackets of the equation (1), we get
 $ \Rightarrow 7-4[3]-4[-(4y+5)] $
Now, we again solve for the brackets, that is we use distributive property $ a(b+c+d)=ab+ac+ad $ , to get
 $ \Rightarrow 7-4[3]-4[-4y]-4[-5] $
Now, we will multiply these numbers, to get
 $ \Rightarrow 7-12+16y+20 $
After this, we will solve addition in the above equation, we get
 $ \begin{align}
  & \Rightarrow +16y-12+7-20 \\
 & \Rightarrow +16y-12-13 \\
\end{align} $
In last, we will apply subtraction in the above equation, we get
 $ \Rightarrow 16y-23 $
Thus, we cannot solve the above equation more, because we see that we are left only with a variable and a constant.
Therefore, the simplified answer to the equation $ 7-4[3-(4y-5)] $ is $ 16y-23 $ , which our required answer is.

Note:
 Always remember the definition of BODMAS because if you do not solve the algebraic equation according to the definition of BODMAS, the answer will be different and is not the correct answer. After this step, $ 7-4[3]-4[-(4y+5)] $ , keep in mind the negative sign with 4. Always do all the steps properly to avoid any error in the solution.