Inequalities: แบบฝึกหัด

Find the number of integers \(n\) that satisfy the inequality:
\(-5 < 2n - 1 \leq 7\)

Identify the list of all integer values of \(n\) that satisfy the double inequality:
\(2n + 3 > -1\) and \(3n - 5 \leq 4\)

Find the set of values of \(x\) for which:
\(2x^2 - 7x + 3 \leq 0\)

Solve the inequality \(4(x - 2) < 12\) and state the largest integer value that satisfies it.

Solve the quadratic inequality \(x^2 - 5x + 6 \leq 0\).

Find the set of integer values of \(x\) that satisfy both the inequality \(x^2 - x - 20 < 0\) and the inequality \(2x + 3 > 1\).

(a) Solve the inequality:
\( 4(x - 2) < 2x + 10 \)

(b) Represent your answer to part (a) on a number line.

Find the set of values for which \(x\) satisfies both of these inequalities:
\(2x + 5 > 1\) and \(x^2 - 4x - 12 < 0\).

Represent your final answer as a single inequality.