Question

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

Answer 1

Hint: Given the inequality expression. We have to solve the expression and find the value of h. First, we will isolate the variable at the one side of the inequality and constant terms on another side. Then, we will simplify the inequality by adding or subtracting the values.

Complete step-by-step answer:
We are given the inequality, $2h + 8 > 3h - 6$. First, we will isolate the variable h on one side of the inequality. We will subtract $3h$ from both sides of the inequality.
$ \Rightarrow 2h + 8 - 3h > 3h - 6 - 3h$
On simplifying the inequality, we get:
$ \Rightarrow - h + 8 > - 6$
Now, we will subtract $8$ from both sides of the inequality.
$ \Rightarrow - h + 8 - 8 > - 6 - 8$
On combining like terms, we get:
$ \Rightarrow - h > - 14$
Now, multiply both sides by $ - 1$ and reverse the inequality symbol.
$ \Rightarrow - h \times \left( { - 1} \right) > - 14 \times \left( { - 1} \right)$
On simplifying the inequality, we get:
$ \Rightarrow h < 14$
Thus, the value of $h$ is the set of all real numbers less than $14$. In the interval notation, the solution is represented as $\left( { - \infty ,14} \right)$

Final answer: Thus, the solution of the inequality is $h < 14$

Additional information: When inequality is solved, then the first aim is to isolate the variable on one side of the inequality and move all constant terms to another side of the inequality. When the solution of the inequality is written in interval form, then the type of bracket inserted depends on the symbol of inequality. If the inequality symbol contains greater than or less than the symbol, then the bracket showing the range of the solution set is always a round bracket. But if the symbols are either greater than equal to or less than equal to, then square brackets are used to show the solution interval.

Note:
 In such types of questions the students mainly don't get an approach on how to solve it. In such types of questions students mainly forget to apply the correct operation on the inequality such that the variable is isolated on one side of the inequality.