How do you graph and solve $| x - 2 | > 1$ ?

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Answer 1 · 2017-05-19T04:16:19

$x<1 " and " x > 3$

Absolute value functions need to be broken into two functions:
$(x-2) > 1 " and " -(x-2) > 1$

Solve for $x$ :

$x -2 + 2 > 1 + 2 " and " -x + 2 > 1$

$x > 3 " and " -x + 2 - 2 > 1 - 2$

$x > 3 " and " -x > -1$

Whenever you divide by a $-1$ you need to switch the direction of the inequality.

$x > 3 " and " -x/-1 < -1/-1$

$x > 3 " and " x < 1$

When graphing use open holes or parentheses to show $< or >$ . Use a solid dot or a bracket to show $<= or >=$

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How do you graph and solve | x - 2 | > 1 | x - 2 | > 1?