Question

Which inequality is true when X= 4 -25x >100 -25x _>100 25x < 100 25<_100

Answer 1

25x ≤ 100

Explanation:

`x=4\\\\-25x>100\qquad\text{change the signs}\\25x<-100\qquad\text{divide both sides by 25}\\x<-4\qquad\bold{NOT}\to4<-4\qquad\bold{FALSE}\\\\-25x\geq100\qquad\text{change the signs}\\25x\leq-100\qquad\text{divide both sides by 25}\\x\leq-4\qquad\bold{NOT}\to4\leq-4\qquad\bold{FALSE}\\\\25x<100\qquad\text{divide both sides by 25}\\x<4\qquad\bold{NOT}\to4<4\qquad\bold{FALSE}\\\\25x\leq100\qquad\text{divide both sides by 25}\\x\leq4\qquad\bold{YES}\to4\leq4\qquad\bold{TRUE}`

Put the value of x = 4 to each inequality:

-25x > 100 → -25(4) > 100 → -100 > 100 FALSE

-25x ≥ 100 → -25(4) ≥ 100 → -100 ≥ 100 FALSE

25x < 100 → 25(4) < 100 → 100 < 100 FALSE

25x ≤ 100 → 25(4) ≤ 100 → 100 ≤ 100 TRUE