How do you solve and graph #abs(u+3)<7#?

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Answer 1 · 2017-12-03T14:10:11

Solution: #color(green)(-10 < u <4)#

Using interval notations our solution can be written as

#color(green)((-10, 4)#

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We are given the inequality

#color(blue)(| u+3 |<7)#

Absolute Inequalities yield two values, one with positive sign and the other with the negative sign.

Hence,

We will rewrite this inequality as

#color(blue)(-7 < u + 3 < +7)#

The above inequality has three parts:

#-7, u + 3, and +7#

We can solve this inequality by subtracting #3# from all the three parts of the inequality.

So, we get,

#color(blue)(-7 - 3< u + 3 - 3 < +7 - 3)#

#color(green)(rArr -10 < u < 4)#

Using interval notations our solution can be written as

#color(green)((-10, 4)#