Inequalities：練習問題

If \(x\) is an integer satisfying the inequality \(-2 \le x < 2\), how many possible values can \(x\) take?

Solve the linear inequality:
$$2(x+3) - 5x \ge 4x + 15$$

Solve the linear inequality:
$$1 - \frac{x - 4}{3} < \frac{5x + 1}{6}$$
If \( x \) is an integer, determine the smallest possible value of \( x \).

Solve the inequality \(5x - 12 > 18\).

Given that \( x \) is an integer satisfying both inequalities \( 2x - 5 < 3(x - 2) \) and \( \frac{k - 3x}{2} \ge 1 \), where \( k \) is a constant. If there are exactly 3 possible values for \( x \), which of the following describes the range of values of \( k \)?

Solve the inequality \( x + 7 < 3 \) and state the result using an inequality sign.

Solve the inequality \( 12 - 3x \le 6 \) and find the smallest integer value of \( x \) that satisfies this inequality.

Solve the inequality \( \frac{3x-2}{5} - \frac{x+4}{2} > -2 \) and find the smallest integer value of \(x\) that satisfies it.

In a classroom, the number of girls is 5 more than twice the number of boys.

(a) If there are \(b\) boys, express the number of girls in terms of \(b\).

(b) The total number of students in the classroom must not exceed 35. Formulate an inequality to represent this situation in terms of \(b\).

(c) Solve the inequality found in part (b).

(d) Given that the number of boys must be a whole number, what is the maximum possible number of boys in the classroom?

If it is given that \( x + 3 < 10 \), find the possible range of the expression \( 2x - 1 \).