Question

What is the solution to this inequality?

7(2m -3/7 ) < 16m + 7

A. M < -5
B. M > -5
C. M < -52/49
D. M > -52/49

Answer 1

To solve the inequality 7(2m - 3/7) < 16m + 7, distribute, combine like terms, isolate the variable m, then solve for m. The solution is M > -5.

Step-by-step explanation:

To solve the given inequality, we need to isolate the variable m on one side of the inequality symbol. Here are the steps:

1. Distribute 7 to both terms inside the parentheses: 14m - 3 < 16m + 7
2. Combine like terms by subtracting 16m from both sides: 14m - 16m - 3 < 16m - 16m + 7
3. Simplify: -2m - 3 < 7
4. Add 3 to both sides: -2m - 3 + 3 < 7 + 3
5. Simplify: -2m < 10
6. Divide both sides by -2. When dividing by a negative number, flip the sign: m > -5

Therefore, the solution to the inequality is M > -5.