Question

solve the linear inequality for n and graph the answer in the number line. then write the solution in inequality notation.
$n - 4 > -2$
show your work here
hint: to add infinity (∞), type \infinity\

Explanation:

Step1: Add 4 to both sides

To solve for \( n \) in the inequality \( n - 4 > -2 \), we add 4 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality sign remains the same.

$$ n - 4 + 4 > -2 + 4 $$

Step2: Simplify both sides

Simplifying the left - hand side, \( n-4 + 4=n \). Simplifying the right - hand side, \( - 2+4 = 2 \). So we get:

$$ n>2 $$

For graphing on the number line: We use an open circle at \( n = 2 \) (because the inequality is \( n>2 \), not \( n\geq2 \)) and draw an arrow to the right to represent all numbers greater than 2.

Answer:

The solution to the inequality \( n - 4>-2 \) is \( n > 2 \). In inequality notation, the solution is \( n>2 \).