Question

1. how do you see it? let m > 0. match each inequality with its graph. explain your reasoning.

a. $\frac{x}{m} < - 1$
b. $\frac{x}{m} > 1$
c. $\frac{x}{m} < 1$
d. $-\frac{x}{m} < 1$
a. ←———————○→
m
b. ←———————○→
m
c. ←——○——————→
-m
d. ←——○——————→
-m

Explanation:

Step1: Solve inequality a

Multiply both sides of $\frac{x}{m}<-1$ by $m$ (since $m > 0$, the inequality - sign remains the same), we get $x<-m$. This corresponds to graph C.

Step2: Solve inequality b

Multiply both sides of $\frac{x}{m}>1$ by $m$ (because $m>0$, the inequality - sign remains the same), we get $x > m$. This corresponds to graph A.

Step3: Solve inequality c

Multiply both sides of $\frac{x}{m}<1$ by $m$ (as $m > 0$, the inequality - sign remains the same), we get $x

Step4: Solve inequality d

Multiply both sides of $-\frac{x}{m}<1$ by $-m$. Since $m>0$, multiplying by $-m$ flips the inequality - sign, we get $x>-m$. This corresponds to graph D.

Answer:

a. C
b. A
c. B
d. D