Answer:
See the attached graph
Explanation:
Take each inequality and isolate x for each
x+1 < 9
==> x + 1 - 1 < 9 -1 add 1 both sides
==> x < 8
4x ≤ 8
==> 4x/4 ≤ 8/4 divide by 4 both sides
==> x ≤ 2
So we have two inequalities to satisfy
To graph,
- Graph each inequality separately
- Choose a test point to determine which side of the line is to be shaded or simply use a graphing calculator to automatically shade
- The solution to the system of equations is the area where the two shadings overlap i.e. values which satisfy both inequalities
To graph the first inequality, draw a vertical line at x = 9 parallel to the y-axis. This line should be dotted to show it is a < inequality. Everything to the left of this line satisfies x < 8
To graph the second inequality, x ≤ 2, draw a vertical line at x = 2 parallel to the y-axis. This line should be solid to show it is a ≤ inequality. Everything to the left of this line satisfies x ≤ 2
The common points for both lines are shown in dark purple in the graph where the two shaded areas overlap
If you just wanted it on the number line that would be the second image