Question

Solve the following equation for x.
$
  3x - 4\left( {3x - 2} \right) = - x \\
  {\text{A}}{\text{. - 1}} \\
  {\text{B}}{\text{. 1}} \\
  {\text{C}}{\text{. 2}} \\
  {\text{D}}{\text{. - 3}} \\
 $

Answer 1

Hint:To solve the given question we must understand the concept of linear equations in one variable and understand that variables can be treated as a number when it comes to solving the equations. Hence, the operations of add, subtract, multiply and divide can be applied to them.

Complete step-by-step answer:

Equation to solve for ${\text{x}}$
${\text{3x - 4}}\left( {3{\text{x - 2}}} \right) = {\text{ - x}}$

Now, subtract ${\text{x}}$ from both sides
$
  3{\text{x - 12x + 8 - x = - x - x}} \\
   \Rightarrow {\text{3x - 13x + 8 = - 2x}} \\
   \Rightarrow {\text{ - 10x + 8 = - 2x}} \\
   \Rightarrow {\text{ - 2x + 10x = 8}} \\
   \Rightarrow {\text{8x = 8}} \\
  {\text{x = 1}} \\
 $

Therefore, the answer is option ${\text{B}}$

Note: We subtracted not a number but a term involving the variable from both sides. We can do this as variables are also numbers. Also, note that subtracting ${\text{x}}$ from both sides amounts to transposing ${\text{x}}$ to LHS. Linear equations with one variable are solved by simplifying them and with variables on both sides we will either subtract or multiply both sides of the equation.