Question

test another value included in the solution set.
-5 ≤ -4 true
x + 3 ≤ -1
-5 + 3 ≤ -1 substitute -5 for x.
-2 ≤ -1

Explanation:

To test another value in the solution set, we first assume the inequality is of the form \( x + 3 \leq -1 \) (from the given substitution \( -5 + 3 \leq -1 \)). Let's pick another value from the solution set of \( x + 3 \leq -1 \). Solving \( x + 3 \leq -1 \), we subtract 3 from both sides: \( x \leq -1 - 3 \), so \( x \leq -4 \). Let's choose \( x = -6 \) (which is less than -4, so in the solution set).

Step 1: Substitute \( x = -6 \) into the inequality

Substitute \( x = -6 \) into \( x + 3 \leq -1 \):
\( -6 + 3 \leq -1 \)

Step 2: Simplify the left - hand side

Calculate \( -6+3 \):
\( -3 \leq -1 \)

We know that - 3 is less than - 1, so the inequality holds true for \( x=-6 \).

Answer:

When we test \( x = - 6\) in the inequality (assuming the inequality is \(x + 3\leq - 1\)), we substitute to get \(-6 + 3\leq - 1\), which simplifies to \(-3\leq - 1\), and this is a true statement.