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

Answer 1

Nathan Axel

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

Using interval notations our solution can be written as

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

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)#

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Answer 2

Nathan Axel

To solve and graph the inequality |u + 3| < 7, you would first isolate the absolute value expression, then consider the two cases: when u + 3 is positive and when it's negative. After finding the solution sets for each case, you would combine them to obtain the overall solution set. Finally, you would graph the solution set on a number line.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and graph #abs(u+3)&lt;7#?

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