Question

How do you solve $x - 8 > 10$?

Answer 1

Hint: Given a linear equation. We have to find the value of variable x by simplifying the inequality. First, we will simplify the left-hand side of the inequality by adding or subtracting some value on both sides of the inequality. Then solve the inequality for a variable.

Complete step-by-step solution:
We are given the linear inequality. First, add $8$ on both sides of inequality to isolate the variable $x$.
$ \Rightarrow x - 8 + 8 > 10 + 8$
On simplifying the inequality, we get:
$ \Rightarrow x > 18$
Therefore, the solution of the inequality includes all real numbers on the number line greater than $18$, but $18$ is not included in the solution set.

Hence, the solution of the inequality is $\left( {18,\infty } \right)$

Note: 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.