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Solve the following inequality algebraically. 5|x + 5| +3 < 28

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Starting with the expression:


5\lvert x+5\rvert+3<28

substract 3 from both sides of the inequality:


5\lvert x+5\rvert<25

divide both sides by 5:


\lvert x+5\rvert<5

There are two cases.

Case 1: x+5 is greater or equal to 0.

In this case, |x+5| = x+5, then:


\begin{gathered} x+5<5 \\ \Rightarrow x<0 \end{gathered}

Since by hypothesis:


x+5\ge0

then also:


-5\le x

Then, for case 1, we have that:


-5\le x<0

Case 2: x+5 is lower than 0

In this case, |x+5|=-x-5, then:


-x-5<5

add x-5 to both sides:

[tex]\begin{gathered} -x-5+x-5<5+x-5 \\ \Rightarrow-10Since x+5 is lower than 0, then:
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