Let's simplify the inequality step by step:
Expand the left side of the inequality:(3x-8)(3x+8) = 9x^2 - 64
Expand the right side of the inequality:(3x-5)² = 9x^2 - 30x + 25(3x-5)² - 29 = 9x^2 - 30x + 25 - 29 = 9x^2 - 30x - 4
So the simplified inequality becomes:9x^2 - 64 ≤ 9x^2 - 30x - 4
Now, let's solve for x:
Subtract 9x^2 from both sides:-64 ≤ -30x - 4
Add 4 to both sides:-60 ≤ -30x
Divide by -30 (remembering to switch the direction of the inequality because we are dividing by a negative number):2 ≥ x
So the solution to the inequality (3x-8)(3x+8)≤ (3x-5)²-29 is x ≤ 2.
Let's simplify the inequality step by step:
Expand the left side of the inequality:
(3x-8)(3x+8) = 9x^2 - 64
Expand the right side of the inequality:
(3x-5)² = 9x^2 - 30x + 25
(3x-5)² - 29 = 9x^2 - 30x + 25 - 29 = 9x^2 - 30x - 4
So the simplified inequality becomes:
9x^2 - 64 ≤ 9x^2 - 30x - 4
Now, let's solve for x:
Subtract 9x^2 from both sides:
-64 ≤ -30x - 4
Add 4 to both sides:
-60 ≤ -30x
Divide by -30 (remembering to switch the direction of the inequality because we are dividing by a negative number):
2 ≥ x
So the solution to the inequality (3x-8)(3x+8)≤ (3x-5)²-29 is x ≤ 2.