Final answer:
After simplifying the given inequality, we find that x ≤ 1. Considering the provided options, -3 and 1 both satisfy the inequality. However, -3 is the only option listed, making it the correct answer.
Step-by-step explanation:
To solve the inequality -2(9x + 3) -7x ≥ -10x - 1(12x + 9), we must first expand the brackets and simplify the expression.
Start by expanding the left side:
- -2 × 9x = -18x
- -2 × 3 = -6
Now, the inequality looks like this:
-18x - 6 - 7x ≥ -10x - 12x - 9
Combine like terms on both sides:
- Left side: Combine -18x and -7x to get -25x.
- Right side: Combine -10x and -12x to get -22x.
The simplified inequality is now:
-25x - 6 ≥ -22x - 9
Next, add 22x to both sides to get:
-3x - 6 ≥ -9
Add 6 to both sides to get:
-3x ≥ -3
Finally, divide by -3, remembering to reverse the inequality (since you're dividing by a negative number), to get:
x ≤ 1
Now we can check the options given to see which is a solution. The correct solution will be less than or equal to 1.
- A) 3 is not a solution because 3 > 1.
- B) -3 is a solution because -3 < 1.
- C) 1 is a solution because 1 = 1.
- D) 2 is not a solution because 2 > 1.
The solutions are -3 and 1, but the options on the question provide only one correct answer, therefore the correct answer is B) -3.