Question

1. \\(\frac{2}{3}z + 1 = 13\\)\
2. \\(\frac{w - 17}{9} = 2\\)

Explanation:

Problem 5: Solve \(\boldsymbol{\frac{2}{3}z + 1 = 13}\)

Step 1: Subtract 1 from both sides

To isolate the term with \(z\), we subtract 1 from both sides of the equation.
\(\frac{2}{3}z + 1 - 1 = 13 - 1\)
\(\frac{2}{3}z = 12\)

Step 2: Multiply both sides by \(\frac{3}{2}\)

To solve for \(z\), we multiply both sides by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\).
\(z = 12\times\frac{3}{2}\)
\(z = \frac{36}{2}\)
\(z = 18\)

Step 1: Multiply both sides by 9

To isolate the numerator, we multiply both sides of the equation by 9.
\(9\times\frac{w - 17}{9} = 2\times9\)
\(w - 17 = 18\)

Step 2: Add 17 to both sides

To solve for \(w\), we add 17 to both sides of the equation.
\(w - 17 + 17 = 18 + 17\)
\(w = 35\)

Answer:

\(z = 18\)

Problem 6: Solve \(\boldsymbol{\frac{w - 17}{9} = 2}\)