Question

Show $\frac{3x-4}{2}\ge \frac{x+1}{4}-1.$ Show the graph of the solutions on number line.

Answer 1

Given $\frac{3x-4}{2}\ge \frac{x+1}{4}-1$

$\Rightarrow \frac{3x-4}{2}\ge \frac{x+1-4}{4}$

$\Rightarrow \frac{3x-4}{2}\ge \frac{x-3}{4}$

$\Rightarrow 4\times \frac{3x-4}{2}\ge x-3$

$\Rightarrow 2(3x-4)\ge x-3$

$\Rightarrow 6x-8\ge x-3$

$\Rightarrow 6x-x\ge -3+8$

$\Rightarrow 5x\ge 5$

$\Rightarrow x\ge 1$

The graphical representation is


Here, $1$ is included in the standard graph.