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# How do you solve $12x - 4 = 32$ ?

Last updated date: 11th Sep 2024
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Hint: As we can see $4$ is common in the left-hand side of the equation we will take $4$ out from the left-hand side. Then we will look at the right-hand side. $\;32$ is the multiplication of $4$ and $8$ . So clearly $4$ will be cut out from both sides. Then we will take the constant part on the right-hand side and keep the variable$x$ on the left-hand side of the equation and then we get the value of $x$.

We have given;
$12x - 4 = 32$
As $\;12$ is the multiplication of $3$ and $4$ so $4$ can be taken as common from the left-hand side. Then the left-hand side of the equation can be written as $4(3x - 1)$ . Hence we get;
$\Rightarrow 4(3x - 1) = 32$
$32$is the multiplication of $4$ and $8$ . Hence we can rewrite the above equation as;
$\Rightarrow 4(3x - 1) = 4 \cdot 8$
So clearly $4$ will be cut out from both side and we will get;
$\Rightarrow 3x - 1 = 8$
Adding $1$ in both side of the equation we get;
$\Rightarrow 3x = 9$
Dividing both sides of the equation with $3$ we get;
$\Rightarrow x = 3$
So the solution is $x = 3$ .
Alternative Method:
We have given;
$12x - 4 = 32$
Adding $4$ in both side of the equation we get;
$\Rightarrow 12x = 36$
Dividing both sides of the equation with $12$ we get;
$\Rightarrow x = 3$

So our required solution is $x = 3$ .

Note: The given equation is called a linear equation. The easiest way to solve the linear equation is to separate the variable and the constant part on both sides of the equation. Students can either divide both sides of the equation with the coefficient with the variable at first or else do addition or subtraction of the constant part first; both of them provide the same result.