How do you solve |\frac { 6} { 3z + 6} | = 8∣∣∣63z+6∣∣∣=8?

2 Answers
José F.
Jan 27, 2018

z=-7/4 or z=-9/4z=−74orz=−94

Explanation:

|6/(3z+6)|=8∣∣∣63z+6∣∣∣=8

|2/(z+2)|=8∣∣∣2z+2∣∣∣=8

2/(z+2)=+8 or 2/(z+2)=-82z+2=+8or2z+2=−8

z+2=2/8 or z+2=-2/8z+2=28orz+2=−28

z=2/8-2 or z=-2/8-2z=28−2orz=−28−2

z=2/8-16/8 or z=-2/8-16/8z=28−168orz=−28−168

z=-14/8 or z=-18/8z=−148orz=−188

z=-7/4 or z=9/4z=−74orz=94

smendyka
Jan 27, 2018

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

6/(3z + 6) = -863z+6=−8

6/(3z + 6) = -8/163z+6=−81

(3z + 6)/6 = -1/83z+66=−18

color(red)(6) xx (3z + 6)/6 = color(red)(6) xx -1/86×3z+66=6×−18

cancel(color(red)(6)) xx (3z + 6)/color(red)(cancel(color(black)(6))) = -color(red)(6)/8

3z + 6 = -3/4

3z + 6 - color(red)(6) = -3/4 - color(red)(6)

3z + 0 = -3/4 - (4/4 xx color(red)(6))

3z = -3/4 - 24/4

3z = -27/4

(3z) xx 1/color(red)(3) = -27/4 xx 1/color(red)(3)

(color(red)(cancel(color(black)(3)))z) xx 1/cancel(color(red)(3)) = -(color(red)(cancel(color(black)(27)))9)/4 xx 1/cancel(color(red)(3))

z = -9/4

Solution 2:

6/(3z + 6) = 8

6/(3z + 6) = 8/1

(3z + 6)/6 = 1/8

color(red)(6) xx (3z + 6)/6 = color(red)(6) xx 1/8

cancel(color(red)(6)) xx (3z + 6)/color(red)(cancel(color(black)(6))) = color(red)(6)/8

3z + 6 = 3/4

3z + 6 - color(red)(6) = 3/4 - color(red)(6)

3z + 0 = 3/4 - (4/4 xx color(red)(6))

3z = 3/4 - 24/4

3z = 21/4

(3z) xx 1/color(red)(3) = -21/4 xx 1/color(red)(3)

(color(red)(cancel(color(black)(3)))z) xx 1/cancel(color(red)(3)) = -(color(red)(cancel(color(black)(21)))7)/4 xx 1/cancel(color(red)(3))

z = -7/4

The Solution Is:

z = {-9/4, -7/4}

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