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

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Answer 1 · 2017-12-03T14:10:11

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

Using interval notations our solution can be written as

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

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We are given the inequality

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

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

Hence,

We will rewrite this inequality as

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

The above inequality has three parts:

$- 7, u + 3, and + 7$ $-7, u + 3, and +7$

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

So, we get,

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

$\Rightarrow - 10 < u < 4$ $color(green)(rArr -10 < u < 4)$

Using interval notations our solution can be written as

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

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