Question

Solve \[8x + 9 = 2x + 12\].

Answer 1

Hint: The above given expression is an example of a two step equation. In order to solve it we need to manipulate the given equation in such a way that we should get $ x $ by itself. In order to get $ x $ by itself we can perform any arithmetic operations on both LHS and RHS equally at the same time such that the equality of the given equation doesn’t change.

Complete step-by-step solution:
Given
\[8x + 9 = 2x + 12..............................\left( i \right)\]
Now in order to solve the given equation we need to solve for $ x $ .
Such that we have to manipulate the given equation in terms of only $ x $ , which can be achieved by performing different arithmetic operations on both LHS and RHS equally.
So to isolate the $ 8x $ term from equation (i) we can subtract $ 9 $ to both LHS and RHS, since subtracting $ 9 $ to the LHS will isolate the term $ 8x $ alone by canceling the term $ + 9 $ .
Subtracting $ 9 $ to both LHS and RHS of equation (i), we get:
\[8x + 9 - 9 = 2x + 12 - 9..........................\left( {ii} \right)\]
Now on solving (ii) we get:
\[
   \Rightarrow 8x = 2x + 3 \\
   \Rightarrow 8x - 2x = 3.......................\left( {iii} \right) \\
 \]
On simplifying (iii) we can write:
 $
   \Rightarrow 8x - 2x = 3 \\
   \Rightarrow 6x = 3 \\
   \Rightarrow x = \dfrac{3}{6} \\
   \Rightarrow x = \dfrac{{3 \times 1}}{{3 \times 2}} \\
   \Rightarrow x = \dfrac{1}{2} = 0.5....................\left( {iv} \right) \\
  $
So on solving\[\;8x + 9 = 2x + 12\], we get $ x = 0.5 $ .
Therefore our final answer is $ x = 0.5 $ .

Note: A two-step equation is an algebraic equation which can be solved in two steps. The equation is said to be true when we find the value of the variable which makes the equation true. We can also check if the value of the variable that we got is true or not by substituting the value of the variable back into the equation and checking whether it satisfies the given equation or not.