Question

Solve the following equation: \[6x + 5 = 2x + 17\]

Answer 1

Hint: Use the technique of taking terms common from the given equation and then solve, then write the equation into simpler expressions and forms. Then after writing it into simplest forms possible, equate it to the right hand side of the equation as given and get the solution.

Complete step-by-step solution:
We are given with the equation \[6x + 5 = 2x + 17\]
Let us shift the terms to one side i.e. let us take the terms of the left hand side of the equation to the right hand side of the equation and then equate it to zero to get the final solution of the equation.
Then, \[6x + 5 - 2x - 17 = 0\]
\[ \Rightarrow 6x - 2x + 5 - 17 = 0 \\
   \Rightarrow 4x - 12 = 0 \]
Now let us take common from the obtained solution and equate it to zero,
\[ \Rightarrow 4(x - 3) = 0\]
\[ \Rightarrow (x - 3) = 0\]
\[ \Rightarrow x = 3\]
Therefore we reached our required solution for the given equation and hence the resultant solution for the equation is \[x = 3\].

Note: It is important that we know various ways, techniques, shortcuts and methods to solve different types of quadratic equations. Middle term factoring, Sridharacharya method or Quadratic formula, graphical methods are some techniques of solving the roots of a quadratic equation.