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Consider the following inequality:

[tex] -3z - 2 \ \textgreater \ -14 [/tex]

Step 1 of 2: Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.


Sagot :

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]