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|w|+3=9 can you explain how to work this problem

the answers are in the back of my book wich are {-6, 6} but I don't know how they got them

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2 Answers

The two bars on either sides of the letter W, means absolute value. This means that W has two values, one on either side of the number line, from 0 to a specific unit(s) on the right and 0 to a specific unit(s) on the left.

Therefore, we have 

i) w+3=9 and

ii)  -w+3=9.


Solving for w in (i) above, we have w=9-3


Solving for w in (ii) above, we have -w=9-3

                                                     -w=6, but w must be positive so dividing through by -1, yields


Hence the answer {-6,6}


lwl + 3 = 9

Subtract 3 from each side to get:

lwl = 6

The bars on each side of the w mean "absolute value".  The absolute value of the number is the number of places that the number is from another number on a number line.  In this case, we are looking for two numbers that are 6 places from 0.  These numbers are 6 and -6.

When you have an absolute value that equals a positive number, then you can say that the variable equals the positive and negative of the number.