SOLUTION: What is the solution of 3|x + 5|<= 6 ?

Question 242418: What is the solution of 3|x + 5|<= 6 ?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To solve simple absolute value equations or inequalities (with just one absolute value):

Isolate the absolute value
Rewrite the absolute value equation/inequality as two equivalent equations/inequalities without an absolute value and separated by "and" or "or". (Use "and" for "less than" absolute value inequalities and use "or" for absolute value equations and for "greater than" absolute value inequalities.)
Solve the pair of equations/inequalities.

So we start by isolating the absolute value. The 3 has to go. We'll divide both sides by 3 giving:

Now we rewrite this as a pair of inequalities. Since this is a "less than" inequality we will separate the two inequalities with "and". Here are the two inequalities for this problem:
and
Note how

the first equality is exactly the same as the absolute value inequality except there is no absolute value.
the left side of the second inequality is the same as the left side of the first inequality.
the inequality symbol of the second inequality is the opposite of the symbol in the first.
how the right side of the second inequality is the opposite of the right side of the first.

This is how you write an absolute value equation/inequality as two equivalent equations/inequalities.

Now we solve the pair of simple inequalities. We just subtract 5 from both sides of both inequalities separately. This results in:
and
This is our solution. In words: All numbers between -3 and -7 inclusive. In interval notation: [-7, -3]
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