Question

How do you solve $ (x + 5) - 2(4x - 1) = 0? $

Answer 1

Hint: First eliminate the constants from left hand side by help of algebraic operations, then when only term with coefficient of $ x $ left on the left hand side then eliminate the coefficient of $ x $ by dividing both sides with the coefficient of $ x $ .

Complete step-by-step answer:
In order to solve the given equation $ (x + 5) - 2(4x - 1) = 0 $ , we need to arrange the terms, that is all the constants should be on the right hand side and all the variables (terms multiplied with $ x $ in this problem) should be on the left hand side of the equation.
We can arrange the equation according to this with the help of algebraic operations,
The given equation is
 $ \Rightarrow (x + 5) - 2(4x - 1) = 0 $
Using the distributive property of multiplication to evaluate the equation,
 $
   \Rightarrow (x + 5) - 2(4x - 1) = 0 \\
   \Rightarrow (x + 5) - (2 \times 4x - 2 \times 1) = 0 \\
   \Rightarrow x + 5 - 8x + 2 = 0 \;
  $
Using the commutative property of addition and subtraction in order to group similar terms that are constants and variables
 $
   \Rightarrow x + 5 - 8x + 2 = 0 \\
   \Rightarrow (x - 8x) + (5 + 2) = 0 \\
   \Rightarrow - 7x + 7 = 0 \;
  $
Now in order to eliminate the constant from left hand side we will subtract the constant from both the sides
 $
   \Rightarrow - 7x + 7 = 0 \\
   \Rightarrow - 7x + 7 - 7 = 0 - 7 \\
   \Rightarrow - 7x + 0 = - 7 \\
   \Rightarrow - 7x = - 7 \;
  $
So we have eliminated the constant from the left hand side, now it’s time to eliminate the coefficient of $ x $ for which we will divide both sides with the coefficient itself.
 $
   \Rightarrow - 7x = - 7 \\
   \Rightarrow \dfrac{{ - 7x}}{{ - 7}} = \dfrac{{ - 7}}{{ - 7}} \\
   \Rightarrow x = 1 \;
  $
Finally, we get the required solution for the equation $ (x + 5) - 2(4x - 1) = 0 $ which is $ x = 1 $
So, the correct answer is “ $ x = 1 $ ”.

Note: We performed the algebraic operations for eliminating terms on both the sides this is because to maintain the balance of the equation and it is a necessary process if you don’t perform the operations to both sides then the result will be different and incorrect.