Question

solve the inequality and graph the solution.\\(-1 > \frac{z}{2} + 1\\)\
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.\
\\(-5\\) \\(-4\\) \\(-3\\) \\(-2\\) \\(-1\\) \\(0\\) \\(1\\) \\(2\\) \\(3\\) \\(4\\) \\(5\\)

Explanation:

Step1: Subtract 1 from both sides

To isolate the term with \( z \), we subtract 1 from both sides of the inequality \(-1 > \frac{z}{2}+1\). This gives \(-1 - 1>\frac{z}{2}+1 - 1\), which simplifies to \(-2>\frac{z}{2}\).

Step2: Multiply both sides by 2

To solve for \( z \), we multiply both sides of the inequality \(-2>\frac{z}{2}\) by 2. Since 2 is a positive number, the direction of the inequality sign remains the same. So, \(2\times(-2)>2\times\frac{z}{2}\), which simplifies to \(-4 > z\) or \(z < - 4\).

Answer:

The solution to the inequality is \(z < - 4\). To graph this, we plot an open circle at \(-4\) (since \(z\) is not equal to \(-4\)) and draw an arrow to the left (indicating all values less than \(-4\)).