Question

Solve and find the value of the term given below:
$50-\left( -40 \right)-\left( -2 \right).$

Answer 1

Hint: To solve the given question above, we will first assume that a=50, b=-40 and c=-2. Thus, we will first solve the term (a-b) and we will find its value, we will assume that its value is equal to x. Then, we will solve the term (x-c) and find its value. The value of the expression $50-\left( -40 \right)-\left( -2 \right).$ will be assumed to be y.

Complete step-by-step answer:
Before solving this question, we are going to assume that a=50, b=-40 and c=-2. Thus the expression in the above question is converted into the following form:
$a-\left( b \right)-\left( c \right)$.
Let the value of this expression be y. Thus, we will get following equation:
$y=a-\left( b \right)-c..........\left( 1 \right)$
So the value of the above expression in the question will be equal to y and we have to find this value of y. For finding this value, we will write the equation (1) as follow:
$\begin{align}
  & \Rightarrow y=a-b-c.........\left( 2 \right) \\
 & \Rightarrow y=\left( a-b \right)-c \\
\end{align}$
Now, first we e will find the of (a-b). Let the value of (a-b) be x. The value of expression (a-b) is calculate as follow:
$\begin{align}
  & x=\left( a-b \right)=\left[ 50-\left( -40 \right) \right] \\
 & \Rightarrow x=50-\left( -40 \right) \\
\end{align}$
Now, here we are going to use a formula which is as shown below:
$p-\left( -q \right)=p+q$
Where, both p and q are positive. In our case p=50 and q=40. Thus, we have:
$\begin{align}
  & \Rightarrow x=50+40 \\
 & \Rightarrow x=90 \\
\end{align}$
Now, form (2), we have:
$\begin{align}
  & \Rightarrow y=a-b-c \\
 & \Rightarrow y=x-c \\
 & \Rightarrow y=90-\left( -2 \right) \\
\end{align}$
Now, here we will again use the formula: $a-\left( -b \right)=a+b.$ So we will get following:
$\begin{align}
  & \Rightarrow y=90+2 \\
 & \Rightarrow y=92 \\
\end{align}$
Thus, the value of term: $50-\left( -40 \right)-\left( -2 \right)=92.$

Note: Instead of calculating (a-b) first, we can also calculate (a-c) first and then equating it to a variably say, d then finding the value of (d-b). This (d-b) will be the value of the expression: $50-\left( -40 \right)-\left( -2 \right).$Thus, we have :
$\begin{align}
  & d=\left( a-c \right) \\
 & \Rightarrow d=50-\left( -2 \right) \\
 & \Rightarrow d=52 \\
\end{align}$
Now,
 $\begin{align}
  & y=d-b \\
 & \Rightarrow y=52-\left( -40 \right) \\
 & \Rightarrow y=52+40 \\
 & \Rightarrow y=92 \\
\end{align}$
We have done this because our expression is $a-\left( b+c \right)$ and the addition of any two numbers is commutative.