Choose the correct solution graph for the inequality.

Question

8x + 2 ≥ 26 or 4x – 6 ≤ –26

Answer 1

The correct solution graph for the inequality is:

To graph 8x + 2 ≥ 26, we start by subtracting 2 from both sides to isolate the variable:

8x + 2 - 2 ≥ 26 - 2

8x ≥ 24

Next, we divide both sides by 8 to solve for x:

(8x)/8 ≥ 24/8

x ≥ 3

Therefore, the solution graph for 8x + 2 ≥ 26 is a line that includes all points to the right of or on the point (3,0).

To graph 4x – 6 ≤ –26, we start by adding 6 to both sides to isolate the variable:

4x – 6 + 6 ≤ –26 + 6

4x ≤ -20

Next, we divide both sides by 4 to solve for x:

(4x)/4 ≤ -20/4

x ≤ -5

Therefore, the solution graph for 4x – 6 ≤ –26 is a line that includes all points to the left of or on the point (-5,0).

The correct solution graph for the inequality is a shaded region on the number line that includes all points from x = -∞ up to and including x = 3 and all points from x = -∞ up to and including x = -5.