Final answer:
To solve the compound inequality, we solve each inequality separately, then combine the results, which gives us b < 4 or b > -2 as the solution set.
Step-by-step explanation:
To solve the compound inequality 6b < 24 or 4b + 12 > 4, we need to solve each inequality separately and then combine the results.
- For the first inequality 6b < 24, divide both sides by 6 to isolate b, which gives us b < 4.
- For the second inequality 4b + 12 > 4, first subtract 12 from both sides to get 4b > -8 and then divide by 4 resulting in b > -2.
- Since the inequalities are joined by 'or', we combine the solutions. The solution set is all b that satisfy b < 4 or b > -2, which includes all numbers less than 4 and all numbers greater than -2.
When we eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable, we can confirm that our solution set accurately represents all possible values for b that satisfy the original inequalities.
Using an inequality symbol helps to visually represent the relationship between the variable and the constants in the inequality.