Question

Which inequality has no solution?
6 (x + 2) greater-than x minus 3
3 + 4 x less-than-or-equal-to 2 (1 + 2x)
Negative 2 (x + 6) less-than x minus 20
x minus 9 less-than 3 (x minus 3)

Answer 1

Answer:

Second option: $3 + 4 x\leq 2 (1 + 2x)$

Step-by-step explanation:

Let's solve for "x" from each inequality:

$a.\ 6 (x + 2)>x-3\\\\6x+12>x-3\\\\6x-x>-3-12\\\\5x>-15\\\\x>\frac{-15}{5}\\\\x>-3$

$b.\ 3 + 4 x\leq 2 (1 + 2x)\\\\3+4x\leq 2+4x\\\\3-2\leq 4x-4x\\\\1\leq 0\  (FALSE.\ IT\ HAS\ NO\ SOLUTION)$

$c.\ -2 (x + 6)<x-20\\\\-2x-12<x-20\\\\-12+20<x+2x\\\\8<3x\\\\x>\frac{8}{3}$

$d.\ x-9<3(x-3)\\\\x-9<3x-9\\\\x-3x<-9+9\\\\-2x<0\\\\x>0$

Answer 2

Answer:

second choice