Answer:
x<=-11/4
Explanation:
To solve the inequality -3 >= -1 - 3/2(-4x + 9), we can follow these steps:
1. Start by simplifying the expression on the right side of the inequality.
-1 - 3/2(-4x + 9) can be rewritten as -1 + (3/2)(4x - 9) using the distributive property.
-1 + (3/2)(4x - 9) simplifies further to -1 + (3/2)(4x) - (3/2)(9) by distributing (3/2) to (4x - 9).
-1 + (3/2)(4x) - (3/2)(9) simplifies to -1 + (6x) - (27/2) by multiplying (3/2) with 4x and 9.
Combining like terms, we get -1 + 6x - 27/2.
2. Now we can rewrite the inequality as -3 >= -1 + 6x - 27/2.
3. To isolate the variable, we can subtract -1 and -27/2 from both sides of the inequality.
-3 - (-1) >= -1 + 6x - 27/2 - (-1) - (-27/2)
-3 + 1 >= -1 + 6x + 1 + 27/2
-2 >= 6x + 29/2
4. Next, we can simplify the expression on the right side of the inequality.
6x + 29/2 can be rewritten as 6x + (29/2).
5. Now we can rewrite the inequality as -2 >= 6x + 29/2.
6. To isolate the variable, we can subtract (29/2) from both sides of the inequality.
-2 - (29/2) >= 6x + 29/2 - (29/2)
-2 - (29/2) >= 6x
7. Simplifying the expression on the left side of the inequality gives:
-4/2 - 29/2 >= 6x
-33/2 >= 6x
8. Finally, we can solve for x by dividing both sides of the inequality by 6.
(-33/2) / 6 >= x
-33/12 >= x
-11/4 >= x
So, the solution to the inequality -3 >= -1 - 3/2(-4x + 9) is x ≤ -11/4.