Question

How do you solve $3\left( 4y-8 \right)=12?$

Answer 1

Hint: As we can see that the given equation you must solve by breaking the number into parts. Because of the distributive property, It helps to make numbers much easier to solve because you are breaking numbers into parts for solving it. In the given problem we have to simplify it as here we have to find the $'y'$ value.

Complete step-by-step answer:
Here,
The given equation,
$\Rightarrow 3\left( 4y-8 \right)=12$
By using distributive property,
Then multiply the $'3'$ to the bracket
We get,
$\Rightarrow 12y-24=12$
After that take the value of $'-24'$ to another side and then add it with it.
$\Rightarrow 12y=12+24$ (Here sign change $'-'$ to $'+'$ as to move other side]
$\Rightarrow 12y=36$
Divide the $36$ to $12$ we get,
$\Rightarrow y=\frac{36}{12}$
$\Rightarrow y=3$
Hence,
After solving the value of $y$ we get is $3.$
Additional Information:
The distributive tells us how to solve expression in the form of $a\left( b+c \right)$ Which is also called a distributive law, of multiplication and division. Normally we see an expression as $4\left( 8+3 \right)$, we just evaluate what is in the bracket first then remaining part solved, $4\left( 8+3 \right)=4\left( 11 \right)=44$
This is the official order of operation rule that we have learned before. But with the distributive property we multiply $4$ by the bracket as $4\left( 8+3 \right)$
$\Rightarrow 4\times 8+4\times 3$
We distribute the $4$ to the $8,$ then again to $3.$ We must need to remember to multiply first, before doing addition.
i.e. $4\times 8+4\times 3=32+12=44$
See we got the same answer. Both methods are correct. You have to use it. But the new method is much easier.

Note:
We usually use the distributive property because the two terms which are in the bracket cannot be added because they are not like terms. If there are similar terms then we must consider it. You also make sure that you have to solve the outside number with the bracket. You only just need to remember the expression in $a\left( b+c \right)$ from showing us distributive property, and multiplying the number immediately outside parentheses with those that are inside after solving this add the products together. i.e. $a\left( b+c \right)=ab+ac$
Some students are confused and wondering why you don’t use the order of operation that you have learnt before it is not wrong operation. You must also use it for solving the problem.