Question

solve the linear inequality for x and graph the answer in the number line. then write the solution in inequality notation.
2 > x - 4
show your work here
hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\
number line with -15, -10, -5, 0, 5, 10, 15, a circle at 0 and a blue line to the right
toggle point toggle line
solution:

Explanation:

Step1: Add 4 to both sides

To isolate \( x \), we add 4 to both sides of the inequality \( 2 > x - 4 \). This gives us \( 2 + 4 > x - 4 + 4 \).

Step2: Simplify both sides

Simplifying the left side: \( 2 + 4 = 6 \). Simplifying the right side: \( x - 4 + 4 = x \). So the inequality becomes \( 6 > x \), or equivalently \( x < 6 \).

Answer:

The solution to the inequality \( 2 > x - 4 \) is \( x < 6 \). To graph this on the number line, we would have an open circle at 6 (since \( x \) is not equal to 6) and a line extending to the left from 6 to represent all values of \( x \) less than 6. In inequality notation, the solution is \( x < 6 \).