Consider the following inequality:4x−3≤−x−64𝑥−3≤−𝑥−6Step 1 of 2 :  Write the solution using interval notation.

Step 1: Break Down the Problem

We start with the given inequality: $4x - 3 \leq -x - 6$

To solve this, we need to isolate $x$ on one side of the inequality.

Step 2: Relevant Concepts

To solve the inequality, we will perform the following algebraic operations:

1. Add $x$ to both sides.
2. Add $3$ to both sides.
3. Divide by the coefficient of $x$ to isolate $x$.

Step 3: Solve the Inequality

1. Add $x$ to both sides: $4x + x - 3 \leq -6$ simplifies to: $5x - 3 \leq -6$

2. Add $3$ to both sides: $5x \leq -6 + 3$ which simplifies to: $5x \leq -3$

3. Divide both sides by $5$: $x \leq -\frac{3}{5}$

Step 4: Verify and Summarize

We found $x \leq -\frac{3}{5}$. This means any number less than or equal to $-\frac{3}{5}$ will satisfy the inequality.

Final Answer

In interval notation, the solution is: $(-\infty, -\frac{3}{5}]$