Question

solve the equation.
\\(\frac{1}{3}(z + 4) - 6 = \frac{2}{3}(5 - z)\\)
use the sketch tool or paper if it helps with your thinking.

Explanation:

Step1: Eliminate denominators by multiplying both sides by 3

Multiply each term in the equation \(\frac{1}{3}(z + 4)-6=\frac{2}{3}(5 - z)\) by 3 to get rid of the fractions.
\(3\times\frac{1}{3}(z + 4)-3\times6 = 3\times\frac{2}{3}(5 - z)\)
Simplify each term: \(z + 4-18=2(5 - z)\)

Step2: Simplify both sides

Simplify the left - hand side: \(z+(4 - 18)=z - 14\)
Simplify the right - hand side: \(2\times5-2z = 10-2z\)
So the equation becomes \(z - 14=10-2z\)

Step3: Add \(2z\) to both sides

Add \(2z\) to each side of the equation \(z - 14=10-2z\) to get all the \(z\) terms on one side.
\(z+2z - 14=10-2z + 2z\)
Simplify: \(3z-14 = 10\)

Step4: Add 14 to both sides

Add 14 to each side of the equation \(3z-14 = 10\)
\(3z-14 + 14=10 + 14\)
Simplify: \(3z=24\)

Step5: Divide both sides by 3

Divide each side of the equation \(3z = 24\) by 3.
\(\frac{3z}{3}=\frac{24}{3}\)
Simplify: \(z = 8\)

Answer:

\(z = 8\)