Question

: Given: Q=7m+3n, R=11-2m, S=n+5, and T=-m-3n+8. How do you simplify R-S+T?

Answer 1

Hint: This type of problem can be solved by substituting. We have been given the values of Q, R, S and T and these values contain m, n and constants. Let us first find R-S. Substitute the values of R and S in the considered expression. Then group all the m terms and n terms. Do necessary calculations and find the value of R-S. Now add T from R-Similarly group all the m terms and n terms and do necessary calculations to find the value of R-S+T which is the required answer.

Complete step by step solution:
According to the question, we are asked to simplify R-S+T.
We have been given that
Q=7m+3n, --------(1)
R=11-2m, --------(2)
S=n+5 ---------(3)
T=-m-3n+8. --------(4)
Now, we have to find R-S+T.
First, let us consider R-S.
Substitute the values of R and S from (2) and (3) respectively.
We get
R-S=11-2m-(n+5)
Using the distributive property that is a(b+c)=ab+ac, we get
R-S=11-2m-n-5
Let us now group all the constants and subtract.
\[\Rightarrow R-S=11-5-2m-n\]
We know that 11-5=6.
Therefore, we get
R-S=6-2m-n. ---------------(5)
Now, we have to add T to expression (5).
Substitute the value of T from equation (4).
\[\Rightarrow R-S+T=6-2m-n+\left( -m-3n+8 \right)\]
On further simplification, we get
\[R-S+T=6-2m-n-m-3n+8\]
Let us group the m and n terms and add them.
\[\Rightarrow R-S+T=6+m\left( -2-1 \right)+\left( -1-3 \right)n+8\]
On further simplification, we get
\[\Rightarrow R-S+T=6+\left( -3 \right)m+\left( -4 \right)n+8\]
\[\Rightarrow R-S+T=6-3m-4n+8\]
Let us now add the constants. We know that 6+8=14.
Therefore, we get
\[R-S+T=14-3m-4n\]

Hence, the simplified value of R-S+T is 14-3m-4n.

Note: We can also solve this problem by directly substituting the values of R, S and T in the given expression and solve instead of splitting and then adding. Avoid calculation mistakes based on sign conventions. It is advisable to first group all the m, n and constants and then adds them to avoid confusion and calculation mistakes.