Question

Solve: $5x-7<3(x+3),1-\frac{3x}{2}\ge x-4$.

Answer 1

Consider the $5x-7<3(x+3)$

$\therefore 5x-7<3x+9$

$\therefore 2x<16$

$\therefore x<8\dots \left(1\right)$

Now, consider $1-\frac{3x}{2}\ge x-4$

$\therefore x+\frac{3x}{2}\le 1+4$

$\therefore \frac{5x}{2}\le 5$

$\therefore x\le 2\dots \left(2\right)$

As the solution is the joint solution of both inequations, the joint solution is $x<8\cap x\le 2⟹x\le 2$

Hence, $x\le 2$ is the required solution.