Question

current skill $ solve and graph the following inequality: $x - 7>27$ inequality: graph: number line options

Explanation:

Step1: Isolate the variable \(x\)

Add \(7\) to both sides of the inequality \(x - 7>27\).
Using the addition property of inequalities (\(a>b\) implies \(a + c>b + c\) for \(c\in\mathbb{R}\)), we get \(x-7 + 7>27+7\).
Simplifying, \(x>34\).

Step2: Graph the solution

On a number - line, we represent the solution.
Since \(x>34\), we draw an open circle at \(x = 34\) (because \(34\) is not included in the solution set, as the inequality is strict, i.e., \(x>34\) not \(x\geq34\)) and draw an arrow to the right of \(34\) to represent all real numbers greater than \(34\).

Answer:

Inequality: \(x>34\)
Graph: Open circle at \(34\) on the number - line with an arrow to the right.