Question

Match the following inequalities to their respective solution sets.

• A. $x\in (-\infty ,-3]$
• B. $x\in (-\infty ,3)$
• C. $x\in [-4,\infty )$
• D. $x\in (-\infty ,5)$

Answer 1

Let's solve the inequalities one by one

$a)-4x\le 16\Rightarrow -4x\times (-1)\ge 16\times (-1)\Rightarrow 4x\ge -16\Rightarrow x\ge -4\Rightarrow x\in [-4,\infty )$

$b)7x-3<32\Rightarrow 7x<32+3\Rightarrow 7x<35\Rightarrow x<5\Rightarrow x\in (-\infty ,5)$

$c)3x+2\ge 4x+5\Rightarrow 3x-4x\ge 5-2\Rightarrow -x\ge 3\Rightarrow -x\times (-1)\le 3\times (-1)\Rightarrow x\le -3\Rightarrow x\in (-\infty ,-3]$

$d)3-5x>6x-30\Rightarrow -5x-6x>-30-3\Rightarrow -11x>-33\Rightarrow -11x\times (-1)<-33\times (-1)\Rightarrow 11x<33\Rightarrow x<3\Rightarrow x\in (-\infty ,3)$