Question

How do you solve $2h + 8 > 3h - 6$?

Answer 1

In this question, we are given an inequality in terms of $h$ and we have been asked to solve for the $h$ in the inequation. You can either shift the terms from one side to the other side or you can add or subtract like terms on both the sides to neutralize the effect. Ultimately, find the value of the variable. You won’t get the exact value but you will get a constant value from which your variable will either be smaller or larger.

Complete step by step answer:
We are given an inequation and we have to solve for $h$ .
$\Rightarrow 2h + 8 > 3h - 6$ …. (given)
Instead of shifting the terms from one side to the other side, I will add the terms with opposite signs to neutralize the effect. Let us see how it is done.
I will add $6$ to both the sides of the equation,
$\Rightarrow 2h + 8 + 6 > 3h - 6 + 6$
Now, you can see that on the right-hand side, the effect has been neutralized and we have shifted the constant to the other side.
On simplifying, we will get,
$\Rightarrow 2h + 14 > 3h$
Now, we will subtract $2h$ from both the sides,
$\Rightarrow 2h - 2h + 14 > 3h - 2h$
Now, on the left-hand side, the effect has been neutralized and the term has been shifted to the right-hand side.
On simplifying, we will get,
$\Rightarrow 14 > h$

Hence, we have got our answer as $h < 14$ .

Note: You can also directly shift the terms to the other side. But if you are the person who gets confused with inequalities, you can use this method of neutralizing the effect. Sometimes, the sign changes its face. For example: if we multiplied one side of $h < 14$ by $- 1$ , we will have to change the face.
$\Rightarrow \left( { - 1} \right)h < 14$
$\Rightarrow - h < 14$ - This is not the same as $h < 14$ and it is wrong.
The correct answer in this case is $- h > 14$.