Question

ear inequality for x and graph the answer in the number line. then write the solut notation.
2 > x - 4
rk here
equalities (<, >, ≤, ≥), type \less\ or \greater\

Explanation:

Step1: Add 4 to both sides

To solve for \( x \) in the inequality \( 2 > x - 4 \), 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 remains the same.
\[
2 + 4 > x - 4 + 4
\]

Step2: Simplify both sides

Simplifying the left - hand side \( 2 + 4 = 6 \) and the right - hand side \( x-4 + 4=x \). So we get:
\[
6 > x
\]
Which can be rewritten as \( x < 6 \)

For graphing on the number line: We have an open circle at \( x = 6 \) (because the inequality is strict, \( x
eq6 \)) and we shade the region to the left of 6 to represent all values of \( x \) that are less than 6.

In interval notation, the solution is \( (-\infty, 6) \)

Answer:

The solution to the inequality \( 2>x - 4 \) is \( x < 6 \). The graph has an open circle at 6 and shading to the left. The interval notation is \( (-\infty, 6) \)