Question

solve the linear inequality for z and graph the answer in the number line. then write the solution in inequality notation.

z + 2 > -3

show your work here

hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

Explanation:

Step1: Isolate the variable \( z \)

Subtract \( 2 \) from both sides of the inequality \( z + 2 > - 3 \).
Using the property \( a>b\Rightarrow a - c>b - c\) (where \(a = z + 2\), \(b=-3\), \(c = 2\)), we get \(z+2-2>-3 - 2\).
Simplify the left - hand side: \(z+2 - 2=z\), and the right - hand side: \(-3-2=-5\).

Answer:

The solution in inequality notation is \(z>-5\). On the number line, we have an open circle at \(z = - 5\) (because the inequality is strict, \(z
eq - 5\)) and the line is shaded to the right of \(z=-5\) (since \(z\) is greater than \(-5\)).