Question

c. \\(\frac{1}{3}(z + 4) - 6 = \frac{2}{3}(5 - z)\\) \\(z = \square\\)

Explanation:

Step1: Eliminate denominators

Multiply both sides by 3 to get rid of the fraction: $3\times[\frac{1}{3}(z + 4)-6]=3\times\frac{2}{3}(5 - z)$
Simplify: $(z + 4)-18 = 2(5 - z)$

Step2: Expand and simplify

Expand the left and right sides: $z + 4-18 = 10 - 2z$
Simplify left side: $z - 14 = 10 - 2z$

Step3: Collect like terms

Add $2z$ to both sides: $z + 2z-14 = 10 - 2z + 2z$
Simplify: $3z-14 = 10$
Add 14 to both sides: $3z-14 + 14 = 10 + 14$
Simplify: $3z = 24$

Step4: Solve for z

Divide both sides by 3: $\frac{3z}{3}=\frac{24}{3}$
Simplify: $z = 8$

Answer:

$z = 8$