The graphical representation of 3x + 4y = 12 is given in the figure below. This line divides the xy-plane in two half planes, I and II. Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). Thus, the solution region of the given inequality is the shaded half plane I including the points on the line. This can be represented as follows.

Answered by Abhisek | 1 year agoSolve each of the following in equations and represent the solution set on the number line \( \dfrac{5x}{4}-\dfrac{4x-1}{3}>1,\) where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.\( \dfrac{5x-8}{3}\geq \dfrac{4x-7}{2}\), where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line. 5x + 2 < 17, where

**(i) **x ϵ Z,

**(ii)** x ϵ R.