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IDENTIFYING INEQUALITIES WITH VARIABLES AS TRUE OR FALSE
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The concepts for this exercise are summarized below.
For a complete discussion, read the text.
(Click here for solutions to the text exercises.)
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 want to think in terms of position on a number line,
as in the previous examples.
Determine if each inequality is ALWAYS TRUE or ALWAYS FALSE.
EXAMPLES:
x-1 < x+1
Answer: Always True
x > x+2
Answer: Always False