Question

Solve and graph the inequalities $ x < 5 $ or $ x > - 1 $ .

Answer 1

Hint: Inequality is used to compare two numbers on the number line by their sizes. It is a relation through which we can make a non-equal comparison between two numbers or other mathematical expressions. In this problem, we have to solve and graph the inequalities given.

Complete step-by-step answer:
n order to solve the inequalities or $ x > - 1 $ , we can examine that in these inequalities x is smaller than $ 5 $ and x is greater than $ - 1 $ and on combining these two inequalities we can also say that, x is smaller than $ 5 $ and is greater than $ - 1 $ , now, we can write the expression as,
 $ 5 > x > - 1 $ or we can also write it as $ - 1 < x < 5 $ . Now, we have to graph the inequality, from the expression we can say that x lie between $ - 1 $ and $ 5 $ and the graph of the inequality becomes,

Note: Mainly, there are two comparison symbols, one is of greater than $ \left( > \right) $ and other one is of smaller than $ \left( < \right) $ and there are other two comparison symbols as well, it is greater than or equal to $ \left( \geqslant \right) $ and smaller than or equal to $ \left( \leqslant \right) $ . For example, we have to make a graph of the inequality like $ - 10 \leqslant x < 10 $ , where one is symbol of smaller than or equal to and one is a symbol of smaller than and this expression can also be written as $ 10 > x \geqslant - 10 $ , here one is a symbol of greater than and other one is of greater than or equal to. Now, to make the graph for these inequalities, we will use filled dot and unfilled dot on the graph, where the filled dot represents that the number is greater/smaller than or equal to and unfilled dot represents that the number is greater or smaller than but not equal to.