Question

Solve the inequality.-3(m/4+3)>4-3/5m

A.m<3 1/4
B.All real numbers are solutions.
C.m<1/4
D.No solutions

Answer 1

To solve the inequality -3(m/4 + 3) > 4 - 3/5m, simplify and isolate the variable m. The solution is m < -260/27.

Step-by-step explanation:

To solve the inequality -3(m/4 + 3) > 4 - 3/5m, we need to simplify and isolate the variable m. Here are the steps:

1. Distribute -3 to both terms inside the parentheses:
   -3(m/4) - 3(3) > 4 - 3/5m
2. Simplify:
   -3m/4 - 9 > 4 - 3/5m
3. Add 3/5m to both sides:
   -3m/4 - 3/5m - 9 > 4
4. Combine like terms:
   (-15m - 12m)/20 - 9 > 4
5. Combine like terms on the left side:
   -27m/20 - 9 > 4
6. Add 9 to both sides:
   -27m/20 > 13
7. Multiply both sides by -20:
   -27m > 260
8. Divide both sides by -27 (remember to flip the inequality sign because we're dividing by a negative number):
   m < -260/27

So the solution to the inequality is m < -260/27.