Question

Which of the following is equivalent to 7-2(x+2)<-4-3(1-x)?

A:-5x<-10
B:-x<-16
C:-2x<17
D:6x<-9

Answer 1

`\large\boxed{A.\ -5x<-10}`

Explanation:

`7-2(x+2)<-4-3(1-x)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\7+(-2)(x)+(-2)(2)<-4+(-3)(1)+(-3)(-x)\\\\7-2x-4<-4-3+3x\qquad\text{combine like terms}\\\\-2x+(7-4)<3x+(-4-3)\\\\-2x+3<3x-7\qquad\text{subtract 3x from both sides}\\\\-5x+3<-7\qquad\text{subtract 3 from both sides}\\\\-5x<-10`