Alright, let's solve the inequality step by step:
Starting with the given inequality:
[tex]\[ -2x - 3 \geq -1 \][/tex]
Step 1: Isolate the term with the variable [tex]\(x\)[/tex].
To do this, we need to move the constant term on the left side to the right side. We will add 3 to both sides of the inequality:
[tex]\[ -2x - 3 + 3 \geq -1 + 3 \][/tex]
[tex]\[ -2x \geq 2 \][/tex]
Step 2: Divide both sides by -2 to isolate [tex]\(x\)[/tex].
Keep in mind that when dividing an inequality by a negative number, you must reverse the inequality sign:
[tex]\[ \frac{-2x}{-2} \leq \frac{2}{-2} \][/tex]
[tex]\[ x \leq -1 \][/tex]
Therefore, the solution to the inequality [tex]\( -2x - 3 \geq -1 \)[/tex] is:
[tex]\[ x \leq -1 \][/tex]
