solve using set builder notation 5[3M-(M+4)]>-2(M-4)
{m|m ____ ____}
To solve the inequality using set builder notation, we need to isolate the variable 'M' on one side of the inequality and express the solution set in set builder notation. Let's solve step by step:
1. Distribute the multiplication to both terms inside the brackets:
5(3M - (M + 4)) > -2(M - 4)
This simplifies to:
15M - (5M + 20) > -2M + 8
2. Remove the parentheses:
15M - 5M - 20 > -2M + 8
3. Combine like terms on both sides:
10M - 20 > -2M + 8
4. Move the variable terms to one side and the constant terms to the other side by adding 2M and 20 to both sides:
10M + 2M > 8 + 20
This simplifies to:
12M > 28
5. Divide both sides of the inequality by 12:
M > 28/12
6. Simplify the fraction 28/12:
M > 7/3
Therefore, the set builder notation for the solution to the inequality is:
{M | M > 7/3}