Question

Write the solution set using interval notation -3(2x-1)<-4[2+3(x+2)]

Answer 1

`\large\boxed{x<-5(5)/(6)\to x\in\left(-\infty,\ -5(5)/(6)\right)}`

Explanation:

`-3(2x-1)<-4\bigg[2+3(x+2)\bigg]\qquad\text{use the distributive property}\\\\(-3)(2x)+(-3)(-1)<-4\bigg[2+(3)(x)+(3)(2)\bigg]\\\\-6x+3<-4\bigg(2+3x+6\bigg)\qquad\text{combine like terms}\\\\-6x+3<-4\bigg(3x+8\bigg)\qquad\text{use the distributive property}\\\\-6x+3<(-4)(3x)+(-4)(8)\\\\-6x+3<-12x-32\qquad\text{subtract 3 from both sides}\\\\-6x+3-3<-12x-32-3\\\\-6x<-12x-35\qquad\text{add}\ 12x\ \text{to both sides}\\\\-6x+12x<-12x+12x-35\\\\6x<-35\qquad\text{divide both sides by 6}\\\\(6x)/(6)<(-35)/(6)`

`x<-(35)/(6)\to x<-5(5)/(6)`