Linear Equations and Inequalities：練習問題

Solve the following linear equation for \( x \):
\( 3(x - 4) = 15 \)

Consider the linear inequality in terms of \( x \):
\( \frac{2x - 7}{3} \ge \frac{3x + 1}{2} \)
Determine the range of values for \( x \) and identify the largest integer value that satisfies this inequality.

A mobile phone plan charges a fixed monthly fee of \$120 plus \$0.50 per minute for calls. If a student wants to keep their total monthly bill between \$150 and \$200 inclusive, what is the range of minutes, \( t \), they can use?

Determine the solution to the inequality:
\( \frac{x}{2} - 3 \le 2 \)

Solve the linear inequality for \( y \):
\( \frac{y}{2} - 3 \le 2 \)

Solve the following linear equation for \( y \):
\( 3y + 11 = 2 \)

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

Find all positive integer solutions for \( x \) that satisfy the inequality \( \frac{x}{2} + \frac{x}{3} < 5 \).

Given the inequality \(3x + 5 \le 17\):
(a) Solve the inequality for \(x\).
(b) State the largest integer value that satisfies the inequality.

Find the range of values of \(x\) that satisfy the following inequality:
\(2(3 - x) < 4x - 12\)