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how do i solve an equation like this |x+2| >(with a line underneath the >) 8

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how do i solve an equation like this |x+2| >(with a line underneath the >) 8

Guest Sep 3, 2014

#1
+91451
+8

It took me a while to work that one out lol

$$|x+2|\ge 8$$

This says "The absolute value of (x+2) is greater than or equal to 8.

This means that x+2 must be further from zero (or equal to) on the number line than 8 as shown on this number line.

So

$$\begin {array}{rlllrll} x+2 &\le& -8\qquad &or& \qquad x+2&\ge& 8 \\ x+2-2 &\le& -8-2\qquad &or& \qquad x+2-2&\ge& 8-2\\ x &\le& -10\qquad &or& \quad \qquad x&\ge& 6\qquad \end{array}$$

Melody  Sep 4, 2014
Sort:

#1
+91451
+8

It took me a while to work that one out lol

$$|x+2|\ge 8$$

This says "The absolute value of (x+2) is greater than or equal to 8.

This means that x+2 must be further from zero (or equal to) on the number line than 8 as shown on this number line.

So

$$\begin {array}{rlllrll} x+2 &\le& -8\qquad &or& \qquad x+2&\ge& 8 \\ x+2-2 &\le& -8-2\qquad &or& \qquad x+2-2&\ge& 8-2\\ x &\le& -10\qquad &or& \quad \qquad x&\ge& 6\qquad \end{array}$$

Melody  Sep 4, 2014

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