Question

How will you solve \[9h - 3 = h\] ?

Answer 1

Hint: The key to find the solution is to always do the same thing on both sides of the equation while keeping the equation balanced. For solving this equation we need to isolate the \[h\] term on one side and constant on the other side of the equation. The elimination method can be used for solving the system of linear equations.

Complete step-by-step solution:
In order to isolate the term containing \[h\] while keeping the equation balanced, we need to add \[3\] to each side of the equation.
\[
   \Rightarrow 9h - 3 = h \\
   \Rightarrow 9h - 3 + 3 = h + 3 \\
 \]
Next add the numbers to simplify
\[9h = h + 3\]
Later on we need to subtract \[h\] from both sides of the equation
\[9h - h + h + 3 - h\]
Now we will combine like terms
\[8h = 3\]
So to get the value of \[h\] divide each side by \[8\]and cancel the term that is both in numerator and denominator
\[
   \Rightarrow \dfrac{{8h}}{8} = \dfrac{3}{8} \\
   \Rightarrow h = \dfrac{3}{8} \\
 \]

Additional information: To solve this problem in a better way it is important to simplify each side of the equation by removing parentheses and combining like terms. Addition or subtraction is used to isolate variable terms on one side of the equation while to solve the variable multiplication or subtraction is used.

Notes: We can also solve this equation by making everything to zero. It is important to remember that to remove the number it is important to decide how to remove it and we need to do the opposite of what is currently done. So if the number is added we need to remove the number and if it is multiplied then we need to divide for removing the number by keeping the equation balanced.