Question

How do you solve the equation $ ax - k = 3(x + h) $ for x?

Answer 1

Hint: First of all take the given expression, and segregate the terms with the variable “x” and the other terms on one side and use the basic mathematical rules for the simplification. When moving any term from one side to another then the sign of the term also changes.

Complete step-by-step solution:
Take the given expression: $ ax - k = 3(x + h) $
Multiply the term inside the bracket and Open the bracket on the right hand side of the equation.
 $ ax - k = 3x + 3h $
Move the term with “x” on the left hand side of the equation from the right hand side and the term without “x” from the left to the right hand side of the equation. When you move any term from one side to another, then the sign of the term also changes. Positive term becomes the negative and the negative term becomes positive.
 $ ax - 3x = 3h + k $
Take multiple common from both the terms on the left hand side of the equation.
 $ \Rightarrow x(a - 3) = 3h + k $
Term multiplicative on one side, if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow x = \dfrac{{3h + k}}{{a - 3}} $
This is the required solution.

Note: Always remember when you move any term from one side to another, the sign of the term also changes. Positive term becomes the negative term and the negative term becomes the positive term. When the term multiplicative on one side is moved to the opposite side then it goes to the denominator. Always be careful about the sign convention of the terms while simplification.