Question

Solve -3+m>=9 or 1+2m<=19. Write the solution using set-builder notation.

Answer 1

To solve the inequalities -3 + m >= 9 and 1 + 2m <= 19, we isolate m in each and join the solutions with 'or'. The solution in set-builder notation is m >= 12 or m <= 9 , capturing all numbers less than or equal to 9 and greater than or equal to 12.

Step-by-step explanation:

The student is asking to solve two inequalities: -3 + m >= 9 and 1 + 2m <= 19. To solve these, we will deal with each inequality separately and then use set-builder notation to express the solution.

For the first inequality, -3 + m >= 9:

1. Add 3 to both sides to isolate m: m >= 9 + 3.
2. Simplify the inequality: m >= 12.

For the second inequality, 1 + 2m <= 19:

1. Subtract 1 from both sides to isolate 2m: 2m <= 19 - 1.
2. Simplify the inequality: 2m <= 18.
3. Divide both sides by 2 to solve for m: m <= 9.

These two inequalities are joined by or, which means we consider solutions that satisfy at least one of the inequalities. In set-builder notation, the solution to the system of inequalities is:

m

This includes all numbers less than or equal to 9 and all numbers greater than or equal to 12.