Question

How do you solve \[x - 7 > 12\] ?

Answer 1

Hint: For any inequality when you are solving you should know the sign of inequality changes when you multiply minus sign both the sides, and the rest solution can be done the same as that for equals sign is done, nor any other assumption should be needed.

Complete step-by-step answer:
The given question is \[x - 7 > 12\]
In the left side of inequality there can be certain simplification, and after simplifying we can direct solve it:
 \[
   \Rightarrow x - 7 > 12 \\
   \Rightarrow x > 12 + 7 \\
   \Rightarrow x > 19 \;
 \]
Here we get the final range of \[x\] that is greater than \[5\] , which implies that the given quantity can have any possible value above \[19\] but not 19.
Range of \[x\] can be written as \[(19,\infty )\] , here open bracket “ \[()\] ” is indicating that the value written in the bracket is not for the quantity \[x\] but the very next closed value after \[19\] is the value of \[x\] , and since infinity is not known so we always provide open bracket for infinity.
So, the correct answer is “x > 19”.

Note: If you are given the equals to sign with inequalities then also the process would be same the only change would be in describing the range of the quantity, that is closed bracket would be used instead of open bracket.
 Inequality basically defines the region of the quantity whosoever for which the inequality is used for, that is it gives you a range of all possible values for the given quantity you are finding for. In this range real as well as complex range also occurs simultaneously.