Question

Graph the solution to the inequality on the number line.

|x+4| ≤ 4

= |x+4| ≤ 4 or |x+4| ≥ -4

there should only be one solution that applies to BOTH
unless it is in opposite directions with no overlap

Answer 1

To graph the solution to the inequality |x+4| ≤ 4 on the number line, the solution set is -8 ≤ x ≤ 0, including the endpoints. A number line should be drawn with a closed interval from -8 to 0.

Step-by-step explanation:

The original inequality is |x+4| ≤ 4. To graph the solution on the number line, we need to consider when the expression inside the absolute value is positive and when it is negative.

For the expression to be positive or zero, x+4 ≤ 4, which simplifies to x ≤ 0. For the expression to be negative, we consider -x-4 ≤ 4, which simplifies to x ≥ -8. The overlap of x ≤ 0 and x ≥ -8 is the solution set, which is -8 ≤ x ≤ 0.

To graph this on the number line, you would draw a line that starts at -8 and ends at 0 with a closed circle at both ends to represent that both -8 and 0 are included in the solution set.

To graph the solution on the number line, we mark -8 with an open circle and shade to the right, and we mark 0 with a closed circle and shade to the left. The shaded region represents the solution to the inequality.