Question

Solve the compound inequality: 2v + 5 ≥ -7 or 4y + 6 < 18. Write the solution in interval notation. If there is no solution, enter 'Ø'.

Answer 1

To solve the compound inequality 2v + 5 ≥ -7 or 4y + 6 < 18, we solve each inequality separately and then combine the solutions by using interval notation.

Step-by-step explanation:

To solve the compound inequality 2v + 5 ≥ -7 or 4y + 6 < 18, we need to solve each inequality separately and then combine the solutions.

First, we solve the inequality 2v + 5 ≥ -7:

1. 
   
3. Subtract 5 from both sides of the inequality: 2v + 5 - 5 ≥ -7 - 5 → 2v ≥ -12
4. 
   
6. Divide both sides of the inequality by 2 to solve for v: 2v/2 ≥ -12/2 → v ≥ -6

Next, we solve the inequality 4y + 6 < 18:

1. 
   
3. Subtract 6 from both sides of the inequality: 4y + 6 - 6 < 18 - 6 → 4y < 12
4. 
   
6. Divide both sides of the inequality by 4 to solve for y: 4y/4 < 12/4 → y < 3

To combine the solutions, we can write the solution in interval notation:

v ≥ -6 or y < 3 can be written as (-∞, -6] ∪ (-∞, 3).