Question

How do you solve $18 = 3(3x - 6)?$

Answer 1

Hint:First open the parentheses with the help of distributive law of multiplication and simplify the terms then send all the constants to the right side of the equation and all the variables to the left side with the help of algebraic operations and after further simplification divide both side with the coefficient of the variable in the equation to get the required solution for the equation.

Formula used:
Distributive law of multiplication is given as following:
$a(b + c) = ab + ac$

Complete step by step answer:
In order to solve the given equation $18 = 3(3x - 6)$, initially we need to open the parentheses with the help of distributive property of multiplication,
$\Rightarrow 18 = 3(3x - 6) \\
\Rightarrow 18 = 3 \times 3x - 3 \times 6$
Simplifying further we will get
$ \Rightarrow 18 = 9x - 18$
Now subtracting $18\;{\text{and}}\;9x$ from both sides of the equation in order to send constants to the right side and variables to the left side of the equation
$ \Rightarrow 18 - 18 - 9x = 9x - 18 - 18 - 9x$
With the help of commutative property grouping similar terms, we will get
$ \Rightarrow (18 - 18) - 9x = (9x - 9x) - (18 + 18)$
Simplifying further, we will get
$ \Rightarrow - 9x = - 36$
Now dividing both the sides with the coefficient of the variable $x\;{\text{i}}{\text{.e}}{\text{.}}\;( - 9)$ we will get,
$
\Rightarrow \dfrac{{ - 9x}}{{ - 9}} = \dfrac{{ - 36}}{{ - 9}} \\
\therefore x = 4 \\ $
Therefore $x = 4$ is the required solution for the equation $18 = 3(3x - 6)$.

Note: You may noticed that we whenever we are performing an algebraic operation whether it is subtraction or division we are performing it with both the sides, this is because to maintain the balance of the equation we have to do it with both sides and it is necessary to perform with both the sides else the result will be incorrect.Commutative property is only applicable for addition and multiplication not for subtraction and division it is only applicable.