In Example 2, in the first paragraph, change the > to < and then complete the meaning of the resulting inequality as in the first sentence. Rewrite the meaning as in the second line.

Data from Example 2

The inequality x + 1 > 0 is true for all values of x greater than −1. Therefore, the values of x that satisfy this inequality are written as x > −1. This illustrates the difference between the solution of an equation and the solution of an inequality. [The solution of an equation normally consists of a few specific numbers, whereas the solution to an inequality normally consists of an interval of values of the variable.] Any and all values within this interval are termed solutions of the inequality. Because the inequality x + 1 > 0 is satisfied only by the values of x in the interval x > −1, it is a conditional inequality.

The inequality x² + 1 > 0 is true for all real values of x, since x² is never negative. Therefore, it is an absolute inequality.