Z5 − z+2 2z+4 =−3 space, startfraction, 5, divided by, z, end fraction, minus, start fraction, 2, z, plus, 4, divided by, z, plus, 2, end fraction, equals, minus, 3 what is the sum of all the possible values for zzz that satisfy the equation above

The sum of all the possible values for z that satisfy the above equation is -5.

Step-by-step explanation:

The given equation is

We need to find the sum of all the possible values for z that satisfy the above equation.

The given equation can be rewritten as

Cancel out common factors.

Add 2 on both sides.

Multiply both sides by -1.

Only z=-5 satisfy the given equation.

Therefore the sum of all the possible values for z that satisfy the above equation is -5.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .