Question

Which of the following options correctly solves the inequality 4 + 8m ≤ 2(2m - 4)?

A) m ≤ -2
B) m ≥ -2
C) m ≤ 2
D) m ≥ 2

Answer 1

To solve the inequality 4 + 8m ≤ 2(2m - 4), distribute the 2, rearrange the equation, and divide both sides by 8 to find m ≤ -0.5.

Step-by-step explanation:

To solve the inequality 4 + 8m ≤ 2(2m - 4), we need to distribute the 2 to the terms inside the parentheses, which gives us 4 + 8m ≤ 4m - 8.

Next, we can rearrange the equation by subtracting 4m from both sides and adding 8 to both sides to isolate the variable. This gives us 4m + 8m - 4m ≤ -8 + 4, which simplifies to 8m ≤ -4.

Finally, we divide both sides of the equation by 8 to solve for m, which gives us m ≤ -0.5.

Therefore, the correct option is A) m ≤ -2.