Question

Solve the given inequality for real x :

$37-(3x+5)\ge 9x-8(x-3)$

Answer 1

$37-(3x+5)\ge 9x-8(x-3)$

$\Rightarrow 37-3x-5\ge 9x-8x+24$

$\Rightarrow 32-3x\ge x+24$

$\Rightarrow -3x-x\ge 24-32$

$\Rightarrow -4x\ge -8$

$-x\ge -2$

Since $x$ is negative, we multiply both sides by $-1$ and change the signs,

$(-1)(-x)\le (-1)(-2)$

$\therefore x\le 2$

Since $x$ is a real number which is less than or equal to $2$

Hence $x\in (-\infty ,2]$ is the solution.