Equations and inequalities：練習問題

Solve the linear equation: \( \frac{x + 3}{2} = 5 \).

Find the solution set for the inequality: \( 7 - 2x \le 15 \).

Solve the simultaneous equations:
\( 2x + y = 7 \)
\( x^2 - y^2 = 8 \)
One of the possible values for \( x \) is:

Find the range of values of \( x \) satisfying both \( 3x - 5 \le 10 \) and \( 2x + 1 > 5 \).

Consider the simultaneous equations below:
\( 3x - 2y = 13 \)
\( x^2 + y^2 = 26 \)
Find the values of \( y \) that satisfy these equations.

Solve the equation \( \frac{3}{x-2} + \frac{1}{x} = 2 \). Give your answers correct to 2 decimal places.

A rectangular plot of land has a length of \( (2x + 3) \) meters and a width of \( (x + 2) \) meters.
(a) Given that the area of the plot is \( 55 \) m\(^2\), form an equation in \( x \) and show that it simplifies to \( 2x^2 + 7x - 49 = 0 \).
(b) Solve the equation to find the value of \( x \) and hence calculate the perimeter of the plot.