An Inequality that is Always True
Consider the inequality ‘$\,x < x + 1\,$’.
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 ‘$\,x < x + 1\,$’ 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.
‘$\,x-1 < x + 1\,$’ is Always True
‘$\,x > x + 2\,$’ is Always False
Master the ideas from this section
by practicing the exercise at the bottom of this page.
When you're done practicing, move on to:
Solving Equations of the Form $\,xy = 0$
by practicing the exercise at the bottom of this page.
When you're done practicing, move on to:
Solving Equations of the Form $\,xy = 0$