# Identifying Inequalities with Variables as True or False

## An Inequality that is Always True

Consider the inequality
‘$\,x \lt x + 1\,$’.
Let
$\,x\,$ be any real number.
Then,
$\,x+1\,$ lies one unit to the right of $\,x\,$ on a number line.
Therefore,
$\,x\,$ *always* lies to the left of $\,x+1\,,$
so the sentence
‘$\,x \lt x + 1\,$’ is always true.

## An Inequality that is Always False

Consider the inequality
‘$\,x -1> x\,$’.
Let
$\,x\,$ be any real number.
Then,
$\,x-1\,$ lies one unit to the left of $\,x\,$ on a number line.
Therefore,
$\,x-1\,$ *never* lies to the right of $\,x\,,$
so the sentence
‘$\,x-1 > x\,$’ is always false.

For these exercises, you should think in terms of position on a number line, as in the previous examples.

## Examples

Determine if each inequality is ALWAYS TRUE or ALWAYS FALSE.