What are the solutions of the inequality? Check the solutions.12 + 10w ≥ 8(w +12)(1 point)Responsesw ≥ –42w ≥ –42w ≥ 48w ≥ 48w ≥ 42w ≥ 42w ≥ 54
To find the solutions of the inequality 12 + 10w ≥ 8(w + 12), we can start by distributing 8 to both terms inside the parentheses:
12 + 10w ≥ 8w + 96
Next, we can combine like terms:
10w - 8w ≥ 96 - 12
2w ≥ 84
Now, we can divide both sides of the inequality by 2 to solve for w:
w ≥ 42
Therefore, the correct solution to the inequality is w ≥ 42.
Let's check if the solution is correct by substituting w = 42 into the original inequality:
12 + 10(42) ≥ 8(42 + 12)
12 + 420 ≥ 8(54)
432 ≥ 432
The equation is true, which verifies that the solution w ≥ 42 is correct.