Questions: Consider the following inequality: 2z < -14 Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.

Consider the following inequality:
2z < -14

Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.

Transcript text: Consider the following inequality: \[ 2 z<-14 \] Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.

Solution

Solution Steps

Step 1: Isolate the variable term

Given the inequality in the form \(ax + b < c\), we first isolate the variable term by subtracting or adding \(b\) to both sides, resulting in \(ax < c - b\).

Step 2: Solve for x

Next, we divide both sides of the inequality by \(a\) to solve for \(x\), taking care to reverse the inequality sign if \(a\) is negative. This results in \(x < \frac{-14 - 0}{2}\).