Question

solve the inequality $x + 3 \leq -1$.
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$$\begin{align*} x + 3 &\\leq -1\\\\ - 3 &\\ - 3 &\\quad\\text{subtract 3 on both sides.}\\\\ x &\\leq -4 \\end{align*}$$

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you subtracted the same value from both sides of the inequality. that means $x \leq -4$ is the solution set of $x + 3 \leq -1$.
test a value included in the solution set.
$-4 \leq -4$ true
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$$\begin{align*} x + 3 &\\leq -1\\\\ \\boldsymbol{\\text{input}} + 3 &\\leq -1 &\\quad\\text{substitute } -4 \\text{ for } x. \\end{align*}$$

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Explanation:

Step1: Subtract 3 from both sides

$x + 3 - 3 \leq -1 - 3$

Step2: Simplify both sides

$x \leq -4$

Answer:

$x \leq -4$