Answer:
[tex] \sf z = - \dfrac{2}{3} [/tex]
Step-by-step explanation:
Solve for z:
[tex] \longrightarrow [/tex] -2(z + 3) = -z - 4(z + 2)
-4(z + 2) = -4z - 8:
[tex] \longrightarrow [/tex] -2(z + 3) = -z -4z - 8
Grouping like terms, -z - 4z - 8 = (-z - 4z) - 8:
[tex] \longrightarrow [/tex] -2(z + 3) = (-z - 4z) - 8
-z - 4z = -5z:
[tex] \longrightarrow [/tex] -2 (z + 3) = -5z - 8
Expand out terms of the left hand side:
[tex] \longrightarrow [/tex] -2z - 6 = -5 z - 8
Add 5z to both sides:
[tex] \longrightarrow [/tex] (5z - 2z) - 6 = (5z - 5z) - 8
5z - 5z = 0:
[tex] \longrightarrow [/tex] (5z - 2z) - 6 = -8
5z - 2z = 3z:
[tex] \longrightarrow [/tex] 3z - 6 = -8
Add 6 to both sides:
[tex] \longrightarrow [/tex] 3z + (6 - 6) = 6 - 8
6 - 6 = 0:
[tex] \longrightarrow [/tex] 3z = 6 - 8
6 - 8 = -2:
[tex] \longrightarrow [/tex] 3z = -2
Divide both sides of 3z = -2 by 3:
[tex] \longrightarrow [/tex] [tex] \sf \dfrac{3}{3}z = - \dfrac{2}{3} [/tex]
[tex] \sf \dfrac{3}{3} = 1 :[/tex]
[tex] \longrightarrow [/tex] [tex] \sf z = - \dfrac{2}{3} [/tex]
