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Solve `5|x+7|=65` :

`|x+7|=13`  dividing both sides by 5.

Now recall the definition of absolute value. `|x|=x` if x>0 and `|x|=-x` if x<0 (read as the opposite of x).

There are two possibilities for the inside of the absolute value bars in order to satisfy the equation. If the...

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Solve `5|x+7|=65` :

`|x+7|=13`  dividing both sides by 5.

Now recall the definition of absolute value. `|x|=x` if x>0 and `|x|=-x` if x<0 (read as the opposite of x).

There are two possibilities for the inside of the absolute value bars in order to satisfy the equation. If the inside is 13 then |13|=13. If the inside is -13, however, then |-13|=13 also. So there are two possible answers:

`x+7=13==>x=6`

`x+7=-13==>x=-20`

So the two answers are 6 and -20.

Cosider the graph of `y=5|x+7|` and y=65:

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An illustration of the letter 'A' in a speech bubbles

The equation 5|x+7|=65 has to be solved for x.

5|x+7|=65

=> |x+7|= 13

|x + 7| = 13

=> x + 7 = 13 and x + 7 = -13

=> x = 6 and x = -20

The solution for the equation 5|x+7|=65 is x = 6 and x = -20

Approved by eNotes Editorial Team