Final answer:
To solve the inequality, isolate the absolute value expression by adding and dividing both sides, then consider two cases to remove the absolute value and solve for b. The solution is -4 ≤ b ≤ 13/3.
Step-by-step explanation:
To solve the inequality 4|1-6b| - 10 ≤ 90, we need to isolate the absolute value expression first. Start by adding 10 to both sides of the inequality:
4|1-6b| ≤ 100
Next, divide both sides of the inequality by 4:
|1-6b| ≤ 25
Now, we can remove the absolute value by considering two cases:
Case 1: 1-6b ≤ 25
Solve for b: 1 ≤ 25+6b; -24 ≤ 6b; -4 ≤ b
Case 2: -(1-6b) ≤ 25
Solve for b: -1+6b ≤ 25; 6b ≤ 26; b ≤ 13/3
Therefore, the solution to the inequality is: -4 ≤ b ≤ 13/3.