Question

3+1/2(3-x) less than -7

Answer 1

`\large\boxed{x>23\to x\in(23,\ \infty)}`

Explanation:

`3+(1)/(2)(3-x)<-7\qquad\text{subtract 3 from both sides}\\\\(1)/(2)(3-x)<-10\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\left((1)/(2\!\!\!\!\diagup_1)\right)(3-x)<(2)(-10)\\\\3-x<-20\qquad\text{subtract 3 from both sides}\\\\-x<-23\qquad\text{change the all signs}\\\\x>23`