Certainly! Let's solve the inequality step by step:
Consider the inequality:
[tex]\[ -3z - 2 > -14 \][/tex]
Step 1: Isolate the term involving the variable [tex]\( z \)[/tex].
To do this, first add 2 to both sides of the inequality:
[tex]\[ -3z - 2 + 2 > -14 + 2 \][/tex]
[tex]\[ -3z > -12 \][/tex]
Step 2: Solve for [tex]\( z \)[/tex].
To isolate [tex]\( z \)[/tex], divide both sides by -3. Remember, dividing by a negative number reverses the inequality sign:
[tex]\[ \frac{-3z}{-3} < \frac{-12}{-3} \][/tex]
[tex]\[ z < 4 \][/tex]
So, the solution to the inequality [tex]\( -3z - 2 > -14 \)[/tex] is:
[tex]\[ z < 4 \][/tex]
Thus, in algebraic notation, the solution is:
[tex]\[ (-\infty < z) \, \& \, (z < 4) \][/tex]
