Question

How do you solve the given inequation $3x+6 > 12$?

Answer 1

Hint: We start solving the problem by subtracting 6 from both sides of the given inequation. We then make the necessary calculations involving subtraction operation and then divide the obtained result with 3 to proceed through the problem. We then make the necessary calculations to get the values of x which satisfies the given equation which is the required solution of the given inequation.

Complete step by step answer:
According to the problem, we are asked to solve the given inequation $3x+6 > 12$.
We have given the inequation $3x+6 > 12$ ---(1).
Now, let us subtract both sides of the equation (1) with 6.
$\Rightarrow 3x+6-6 > 12-6$.
$\Rightarrow 3x > 6$ ---(2).
Now, let us divide the both sides of the equation (2) with 3.
$\Rightarrow \dfrac{3x}{3} > \dfrac{6}{3}$.
$\Rightarrow x > 2$ ---(3).
From equation (3), we can see that x includes all the real values that were greater than 2. We know that the representation of all the real numbers that were greater than r is $\left( r,\infty \right)$.
So, the representation of the result in equation (3) is $\left( 2,\infty \right)$.

$\therefore $ The solution set (i.e., the values of x satisfying) the given equation $3x+6>12$ is $\left( 2,\infty \right)$.

Note: Whenever we get this type of problems, we try to convert the equation to $x > < a$ by making the multiplication, division and subtraction to get the required result. We can also solve the given problem by representing all the given values on the number line. We should not report the obtained solution as $\left[ 2,\infty \right)$, because this includes 2 in the final solution set which is the common mistake done by students. Similarly, we can expect problems to solve the inequation $3x+3 < 9$.