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

Multiply all terms by 3:
$$3\times\frac{1}{3}(z+4) - 3\times6 = 3\times\frac{2}{3}(5-z)$$
Simplify to get:
$$z + 4 - 18 = 2(5 - z)$$

Step2: Simplify both sides

Combine constants on left, expand right:
$$z - 14 = 10 - 2z$$

Step3: Isolate z terms

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

Step4: Isolate constant terms

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

Step5: Solve for z

Divide by 3:
$$z = \frac{24}{3}$$

Answer:

$z=8$