Question

How do you solve $12(x - 4) = 144$ using the distributive property?

Answer 1

Hint: First we will take all the like terms to one side and then all the alike terms to the other side. Then we will combine the terms on the right side. Then we will add or subtract terms from both the sides according to the requirement and hence evaluate the value of the variable.

Complete step by step answer:
We will start by mentioning the distributive law.
The distributive law states that,
$a \times (b + c) = a \times b + a \times c$
Now apply the distributive law to the given equation and open the brackets along with their respective signs.
$
\Rightarrow 12(x - 4) = 144 \\
\Rightarrow 12x - 48 = 144 \\
\Rightarrow 12x = 192 \\
 $
Now divide both the sides by $12$.
$
\Rightarrow 192 \\
\Rightarrow x = \dfrac{{192}}{{12}} \\
\Rightarrow x = 16 \\
 $
Hence, the value of $x$ is $16$.

Additional information: When we solve an equation, we figure out what value will make the statement true. Most equations are harder to solve and you have to simplify the equation before you can see the solution. The value of the variable which satisfies the equation is called the solution of the equation. An inverse operation is an operation that reverses the effect of another operation. Addition and subtraction are inverses of each other, just like division and multiplication are inverses.

Note: While rearranging the terms, make sure you arrange all the like terms separately and all the alike terms separately with their respective signs. When you are opening the brackets, multiply the signs as well. When you add or subtract any value make sure you do that on both sides so that the equation remains balanced.