solve using set builder notation
-8-11(3x+7)less than or equal to -40x-9
-8-33x-77<=-40x-9
add 40x to each side, then add 85 to each side.
7x<=73
solve for x
To solve the inequality -8 - 11(3x + 7) ≤ -40x - 9, we can start by simplifying the inequality:
-8 - 11(3x + 7) ≤ -40x - 9
-8 - 33x - 77 ≤ -40x - 9
-33x - 85 ≤ -40x - 9
Next, let's simplify further by getting rid of the parentheses:
-33x - 85 ≤ -40x - 9
-33x - 85 + 40x ≤ -9
Now, combine like terms:
-33x + 40x - 85 ≤ -9
(40 - 33)x - 85 ≤ -9
7x - 85 ≤ -9
Add 85 to both sides to isolate the variable:
7x - 85 + 85 ≤ -9 + 85
7x ≤ 76
Divide both sides by 7 to solve for x:
(7x)/7 ≤ 76/7
x ≤ 10.85714285714286
Now we can express the solution using set builder notation:
x ≤ {x | x ≤ 10.85714285714286}