To solve this inequality, we need to first find the critical points by setting each factor equal to zero:
x - 5 = 0 x = 5
x + 5 = 0 x = -5
3x + 5 = 0 3x = -5 x = -5/3
Now we can use these critical points to create intervals on the number line and test each interval to see when the expression is greater than zero.
Interval 1: (-∞, -5) Pick x = -6 (-6 - 5)(-6 + 5)(3(-6) + 5) = (-11)(-1)*(-13) = 143 Since 143 > 0, this interval satisfies the inequality.
Interval 2: (-5, -5/3) Pick x = -4 (-4 - 5)(-4 + 5)(3(-4) + 5) = (-9)(1)*(-7) = 63 Since 63 > 0, this interval satisfies the inequality.
Interval 3: (-5/3, 5) Pick x = 0 (0 - 5)(0 + 5)(30 + 5) = (-5)(5)*(5) = -125 Since -125 is not greater than 0, this interval does not satisfy the inequality.
Interval 4: (5, ∞) Pick x = 6 (6 - 5)(6 + 5)(36 + 5) = (1)(11)*(23) = 253 Since 253 > 0, this interval satisfies the inequality.
Therefore, the solution to the inequality is x ∈ (-∞, -5) ∪ (-5, -5/3) ∪ (5, ∞).
To solve this inequality, we need to first find the critical points by setting each factor equal to zero:
x - 5 = 0
x = 5
x + 5 = 0
x = -5
3x + 5 = 0
3x = -5
x = -5/3
Now we can use these critical points to create intervals on the number line and test each interval to see when the expression is greater than zero.
Interval 1: (-∞, -5)
Pick x = -6
(-6 - 5)(-6 + 5)(3(-6) + 5) = (-11)(-1)*(-13) = 143
Since 143 > 0, this interval satisfies the inequality.
Interval 2: (-5, -5/3)
Pick x = -4
(-4 - 5)(-4 + 5)(3(-4) + 5) = (-9)(1)*(-7) = 63
Since 63 > 0, this interval satisfies the inequality.
Interval 3: (-5/3, 5)
Pick x = 0
(0 - 5)(0 + 5)(30 + 5) = (-5)(5)*(5) = -125
Since -125 is not greater than 0, this interval does not satisfy the inequality.
Interval 4: (5, ∞)
Pick x = 6
(6 - 5)(6 + 5)(36 + 5) = (1)(11)*(23) = 253
Since 253 > 0, this interval satisfies the inequality.
Therefore, the solution to the inequality is x ∈ (-∞, -5) ∪ (-5, -5/3) ∪ (5, ∞).