Question

How will you solve \[{\text{9c(c - 11) + 10(5c - 3) = 3c(c + 5) + c(6c - 3) - 30}}\] ?
\[
  A) 2 \\
  B) 0 \\
  C) 3 \\
  D) 9 \\
 \]

Answer 1

Hint: Since we need to find the value of \[c\] remember we will always do the same thing on both sides of the equation while keeping the equation balanced. The given system of equations can be solved using elimination method and this deals with linear equations with one unknown. Later on fill the value of in equation \[c\] to recheck whether the solution is correct.

Complete step-by-step solution:
At first we will rearrange the equation by subtracting what is to the right of the equal sign from each side of equation
\[9c(c - 11) + 10(5c - 3) - (3c(c + 5) + c(6c - 3) - 30 = 0\]
Now after pulling out like terms
\[
   \Rightarrow 6c - 3 = 3(2c - 1) \\
   \Rightarrow ((9c(c - 11)) + 10(5c - 3))) - (((3c(c + 5)) + 3c(2c - 1)) - 30) = 0 \\
   \Rightarrow ((9c(c - 11)) + 10(5c - 3)) - (9{c^2} + 12c - 30) = 0 \\
   \Rightarrow - 61c = 0 \\
 \]
Later on we will multiply each sides of the equation by \[ - 1\]
\[61c = 0\]
Lastly we will divide each sides of the equation by \[61\]
\[c = 0\]
Therefore the value of \[c\]is \[0\]

Thus the correct answer is option ‘B’.

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. 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.

Note: It is noticed that for the equation above without \[0\] no matter what number we put we will not get the same answers from both sides. We will check by substituting the value of \[c\] in the given equation and we found that the value came out to be the same. Hence it is verified that our solution is correct.