Find the interval satisfying the inequality: 𝒙+𝟏𝟑 ≤ (𝟐𝒙 − 𝟏𝟑) − 𝟑𝒙

Sure, let's solve the inequality step by step:

1. First, let's simplify the inequality: x + 13 ≤ 2x - 13 - 3x
2. Combine like terms on the right side: x + 13 ≤ -x - 13
3. Now, let's get all the x terms on one side and the numbers on the other side. We can do this by adding x to both sides and adding 13 to both sides: x + x ≤ -13 + 13
4. This simplifies to: 2x ≤ 0
5. Finally, divide both sides by 2 to solve for x: x ≤ 0

So, the interval that satisfies the inequality is (-∞, 0].