Question

consider the following inequality. -3z + 2 > -10 step 1 of 2: solve the linear inequality for the given variable. simplify and express your answer in algebraic notation. answer 7 points ers satisfy the inequality, select all real numbers. if no real number satisfies the inequality, select no solution. f the alternative options will replace the entered value(s) with the selected value. otherwise, the entered answer is used. no solution all real numbers

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( z \), we subtract 2 from both sides of the inequality \( -3z + 2 > -10 \). This gives us \( -3z + 2 - 2 > -10 - 2 \), which simplifies to \( -3z > -12 \).

Step2: Divide by -3 (and reverse inequality)

When dividing an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \( -3z > -12 \) by -3, we get \( \frac{-3z}{-3} < \frac{-12}{-3} \), which simplifies to \( z < 4 \).

Answer:

\( z < 4 \)