Linear equations and inequalities

Solve the following inequality assuming positive integer \(x\). \[ 1\frac{1} {3}\leq -\frac{x - 4} {2} \]

Find the set of all the positive integers \(x\) for which the expression \(\frac{3x-7} {14} \) is smaller than \(\frac{7-2x} {7} \).

Consider a coil composed from a ferrite core and a wire winding. The mass of the core is \(2\, \mathrm{kg}\). The material for the wire is such that the mass of the wire of the length \(30\, \mathrm{m}\) is bigger than the mass of the wire of the length \(10\, \mathrm{m}\) together with the ferrite core. In the following list identify a possible mass of one meter of the wire.

Solve the following inequality: \[ \left (5 + 2x\right )\cdot \left (-3\right ) + 16 < 20 - 6x \]