Question

How do you solve $3\left( 3w-4 \right)=-20$ ?

Answer 1

Hint: At first, we apply distributive property to the $3\left( 3w-4 \right)$ term and break it down by opening the bracket. After that, we take the algebraic terms to the left side and the arithmetic terms to the right side and then perform the addition, multiplication, division as required by the problem.

Complete step by step solution:
The given that we have is,
$3\left( 3w-4 \right)=-20$
We start off the solution by applying the distributive property to the first term of the equation. The distributive property states that an expression of the form $a\left( b+c \right)$ can be written as $ab+ac$ . By comparing the first term of the above equation with the general form, we get,
$a=3,b=3w,c=-4$
Thus, applying the distributive property, it becomes, $3\left( 3w-4 \right)=3\times 3w+3\times \left( -4 \right)$ which upon simplification gives, $9w-12$ . Thus, the equation can be rewritten as,
$\Rightarrow 9w-12=-20$
Adding $12$ to both sides of the above equation, the above equation thus becomes,
$\Rightarrow 9w-12+12=-20+12$
This upon simplification gives,
$\Rightarrow 9w=-8$
Dividing both sides of the above equation by $9$ , the equation thus becomes,
$\Rightarrow \dfrac{9w}{9}=\dfrac{-8}{9}$
This upon simplification gives,
$\Rightarrow w=-\dfrac{8}{9}$
Therefore, we can conclude that the solution of the given equation is $w=-\dfrac{8}{9}$ .

Note: In this problem, we can also start solving by dividing both sides of the equation by $3$ at first and then make necessary additions and subtractions. We must be careful while applying the distributive property as students often overlook the signs of the terms inside the brackets and end up in wrong answers. Also, it is advisable not to convert the fractions into decimals as this lowers the accuracy of the answer for recurring decimals. Fractions can be converted to decimals preferably at the end.