solve the inequalites |4m+8|<12. can you show me the calculations.

Expert Answers

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Solve:  `|4m+8| < 12`

This means that 4m + 8 is less than 12 units from 0 on a number line, therefore: 

`4m + 8 < 12and 4m + 8 > -12`

Solve each.

`4m + 8 < 12` Subtract 8.

`4m < 4` Divide by 4.

`:. m < 1`

`4m + 8 > -12` Subtract 8.

`4m > -20` Divide by 4.

`:. m > -5`

This makes a final answer of:  `-5 < m < 1`

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Hi, Quddoos,

For this problem, you would split the inequality up into two inequalities, or a compound inequality.  When the inequality points toward the absolute value like this, the formula is:

|ax+b| < c   becomes

-c < ax+b < c

So, for us, c = 12, a = 4, and b = 8.  So, we have:

-12 < 4x+8 < 12

Then, we solve this for x:

-12 < 4x+8 < 12

-8         -8         -8

-20  <   4x    < 4

   /4        /4        /4

-5  <  x  <  1

So, the answer is -5 < x < 1.

Good luck, quddoos, I hope this assists.

Till Then,

Steve

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