Question

How do you solve \[p - 1 = 5p + 3p - 8\]?

Answer 1

Hint: Here in this we have to solve the given equation and it is in the form of algebraic expression. Solving this equation, we have to find the unknown value p. The LHS of the given equation and the RHS of the equation contains p by using the simple arithmetic operation we find the value of p.

Complete step-by-step solution:
The given equation is an algebraic equation. The algebraic equation is a combination of variable and constant. So we use simple arithmetic operation we solve for further
Now consider the given equation
\[p - 1 = 5p + 3p - 8\]
Add 5p and 3p in the RHS of the above equation
\[ \Rightarrow p - 1 = 8p - 8\]
Take p to the RHS and -8 to the LHS we have
\[ \Rightarrow - 1 + 8 = 8p - p\]
On simplifying we get
\[ \Rightarrow 7p = 7\]
Divide the above equation by 7 we get
\[ \Rightarrow p = 1\]
Therefore, the value of p is 1.
The above equation can be solved in the other procedure also.
Now consider the given equation
\[p - 1 = 5p + 3p - 8\]
Take the terms involving p to RHS and the constant terms to LHS
\[ \Rightarrow - 1 + 8 = 5p + 3p - p\]
Take p as a common in the RHS of the above equation
\[ \Rightarrow - 1 + 8 = p(5 + 3 - 1)\]
On simplifying we get
\[ \Rightarrow 7 = 7p\]
Dividing the above equation by 7 we get
\[ \Rightarrow p = 1\]
We can also verify the given question by substituting the value of p.
Consider \[p - 1 = 5p + 3p - 8\]. Substitute the value of p as 1 so we have
\[ \Rightarrow 1 - 1 = 5(1) + 3(1) - 8\]
On simplification we get
\[
   \Rightarrow 0 = 5 + 3 - 8 \\
   \Rightarrow 0 = 0 \\
 \]
Hence LHS is equal to RHS.

Note: If the algebraic expression contains only one unknown, we determine the value by using simple arithmetic operations like addition, subtraction, multiplication and division. The tables of multiplication should be known to solve these kinds of problems. The problem can be checked or verified by substituting the value which we have obtained.