-2(z+3)-z=-z-4(z+2)
solve for z quickly please! will give brainliest

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]

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