Question

If x belongs to set of integers, A is the solution set of $2(x-1)<3x-1$ and B is the solution set of $4x-3\le 8+x$, find A$\cap$B.

• A. $\{0,1,2\}$
• B. $\{1,2,3\}$
• C. $\{0,1,2,3\}$
• D. $\{0,2,4\}$

Answer 1

Answer: (C)

$\{0,1,2,3\}$

$2(x-1)<3x-1$

$\Rightarrow 2x-2<3x-1$

$\Rightarrow 2x-3x<-1+2$

$\Rightarrow -x<1$

$\Rightarrow x>-1$

$4x-3\le 8+x$

$4x-3-x+3\le 8+x-x+3$

$\Rightarrow 4x-x\le 8+3$

$\Rightarrow 3x\le 11$

$x\le \frac{11}{3}\Rightarrow x\le 3.67$

Then $-1<x\le 3.67$

Then, $A\cap B$ is $\{0,1,2,3\}$