Factorization and Algebraic Fractions：練習問題

Simplify the algebraic expression: \( 3(2x - 5) - 4(x + 2) \).

The figure shows a rectangle with the given side lengths. If the perimeter of the rectangle is \( 38 \) units, find the value of \( x \).

Solve the following equation for \( x \):
\( \frac{2x - 1}{3} - \frac{x + 4}{2} = 1 \)

Solve the following linear equation for \( x \):
\( \frac{x}{4} + 7 = 12 \)

Find the value of \( y \) that satisfies the equation:
\( 5(y - 2) = 2(y + 7) \)

A rectangular garden has a length that is \( 7 \) meters longer than its width. Given that the area of the garden is \( 60 \text{ m}^2 \), find its perimeter in meters.

A cyclist travels from town A to town B, a distance of \(30\) km. On the return journey from B back to A, the cyclist increases their average speed by \(5\) km/h. If the return journey takes exactly \(1\) hour less than the outward journey, calculate the cyclist's average speed for the outward journey in km/h.