Question

solve the inequality $x + 3 \leq -1$.
$x + 3 \leq -1$
$-3 \\ \\ \\ -3$
$x \leq -4$
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 not included in the solution set.
$-3 \leq -4$ \\ \\ false
test another value in
$-5 \leq -4$ \\ \\ true
$x + 3 \leq -1$
$? \\ \\ + 3 \leq -1$ \\ \\ substitute $-3$ for $x$.
$x + 3 \leq -1$
$-5 + 3 \leq -1$
$-2 \leq -1$

Explanation:

Step1: Substitute -3 for x

We are testing the value -3 (which is not in the solution set \( x \leq -4 \)) in the inequality \( x + 3 \leq -1 \). So we substitute \( x=-3 \) into the left - hand side of the inequality.
The left - hand side becomes \( -3+3 \).

Step2: Simplify the left - hand side

\( -3 + 3=0 \). Now we check if \( 0\leq - 1 \). Since 0 is greater than - 1, the statement \( -3 + 3\leq -1 \) (i.e., \( 0\leq -1 \)) is false, which is consistent with -3 not being in the solution set. But for the substitution step, when we substitute \( x = - 3 \) into \( x+3 \), we get \( -3+3 \).

Answer:

When substituting - 3 for \( x \) in \( x + 3\leq - 1 \), the left - hand side is \( -3+3 = 0 \), and the inequality \( 0\leq - 1 \) is false (which is used to test that - 3 is not in the solution set \( x\leq - 4 \)). The value to put in the "?" box is - 3.