Question

4(b-5) ≥ 2(2b-12)

A. b ≥ -20 (b is greater than or equal to negative 20)

B. All real numbers

C. b ≥ -24 (b is greater than or equal to negative 24)

D. No solution

Answer 1

To solve the inequality 4(b-5) ≥ 2(2b-12), distribute the numbers and simplify the expression. The inequality holds true for all values of b, so the answer is All real numbers.

Step-by-step explanation:

To solve the inequality 4(b-5) ≥ 2(2b-12), we need to distribute the numbers and simplify the expression. Starting with the left side:

4(b-5) = 4b - 20

Next, simplify the right side:

2(2b-12) = 4b - 24

Now, we have the inequality: 4b - 20 ≥ 4b - 24

By subtracting 4b from both sides, we get: -20 ≥ -24

Since -20 is greater than or equal to -24, the inequality holds true for all values of b. Hence, the correct answer is B all real numbers, as the inequality holds irrespective of the values plugged into b.