4-3|m+2|=-12 how do you solve for the absolute value?

0) 4-3|m+2| = -12

1) -3|m+2| = -12-4

2) |m+2| = (-12-4)/3
|m+2| = -16/3

3) m+2 = -16/3 or m+2 = 16/3

4) m = -16/3 - 2 or m = 16/3 -2


If you want a more general answer, when you have an absolute value of anything, pretend that it is a variable and solve for it...

4-3|m+2| => 4-3x

Then solve for the new "x"

x = -16/3 => |m+2| = -16/3

Then you can take away the absolute value sign and make the other side positive or negative.

m+2 = ±16/3

Then just solve.

4 - 3|m + 2| = -12
-3|m + 2| = -12 - 4
-3|m + 2| = -16
|m + 2| = -16/-3
|m + 2| = 16/3
m + 2 = ±16/3

m + 2 = 16/3
m = 16/3 - 2
m = 16/3 - 6/3
m = 10/3

m + 2 = -16/3
m = -16/3 - 2
m = -16/3 - 6/3
m = -22/3

∴ m = -22/3 , 10/3

16 = 3 | m + 2 |

16 / 3 = | m + 2 |

m + 2 = 16/3 , m + 2 = - 16/3

m = 10/3 , m = - 22/3

4 - 3 |m + 2| = 12
-3 |m + 2| = -12 - 4 = -16
|m + 2| = -16/-3 = 16/3

So... Either |m + 2| = 16/3
m + 2 = 16/3
m = 16/3 - 2 = 10/3

OR

|m + 2| = -16/3
m = -16/3 - 2
m = -22/3

I hope that helps. :)

me07.

P.S. DO NOT multiply |m + 2| by -3. That'll change the absolute value. Instead, divide the RHS by -3.

there are two cases:

first case .........4-3(m+2)=-12
4-6+12=3m
m= 10/3

second case........4 +3(m+2) = -12
4+6+12 = -3m
22 = -3m
m = -22/3

the absolute value in this case tells you the values of m that are needed so that the function 4-3|m+2| intersects with the horizontal line Y=-12

the graph of this function has its origin in y=-2 with two divirging lines with gradient -3. it is in upside down v.

absolute value is just the amount of numbers between the number and 0. so -12 is 12. 12 is 12. 1 is 1. -167 is 167

using order of operations:

4-(3|m+2|)=-12
-(3|m+2|)=-16
3|m+2|=16
|m+2|=16/3
m+2=+/-16/3

absolute value means that the other side of the equation is positive or negative.

3 - 3|m+2| = -12

subtract three

-3|m+2| = -15

divide by -3

|m+2| = 5

there ya go