Question

solve the inequality. graph and check your solution. -\frac{5}{4}m < - 5 m dropdown box (simplify your answer.)

Explanation:

Step1: Isolate the variable m

Multiply both sides by $-\frac{4}{5}$. When multiplying an inequality by a negative number, the inequality sign flips. So we have $m > (-5)\times(-\frac{4}{5})$.

Step2: Calculate the right - hand side value

$(-5)\times(-\frac{4}{5}) = 4$. So $m>4$.

Answer:

$m > 4$

To graph: Draw a number line. Mark a open circle at 4 (open because 4 is not included in the solution set) and shade the line to the right of 4. To check, pick a value greater than 4, say $m = 5$. Substitute into the original inequality: $-\frac{5}{4}\times5=-\frac{25}{4}=- 6.25$ and $-6.25<-5$, which is true.