Question

How do you solve the equation $3x + 6 = 3(x - 5)?$

Answer 1

Hint: In this solution first of all we will open the bracket on the right hand side of the equation and then will move all the terms on the left hand side of the equation. When you move any term from one side to another sign of the term also changes.

Complete step-by-step solution:
Take the given expression: $3x + 6 = 3(x - 5)$
Multiply the term and open the bracket on the right hand side of the equation.
$3x + 6 = 3x - 15$
Move all the terms on the left hand side of the equation from 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 negative and negative term becomes positive.
$ \Rightarrow 3x + 6 - 3x + 15 = 0$
Arrange like terms together.
$ \Rightarrow \underline {3x - 3x} + \underline {6 + 15} = 0$
Like terms with equal value and the opposite sign cancel each other, simplify the above equation.
$ \Rightarrow 6 + 15 = 0$
Perform addition –
$ \Rightarrow 21 = 0$
Above equation is not possible
But in actual $21 \ne 0$and so the given equation has no solution.

Note: Always remember that like terms with the same value and opposite sign cancel each other. Remember following rules While doing simplification -
i) Addition of two positive terms gives the positive term
ii) Addition of one negative and positive term, you have to do subtraction and give signs of bigger numbers, whether positive or negative.
iii) Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.