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To graph the inequality 4x - 9 ≥ -21, we can start by solving it as an equation to find the boundary line.
4x - 9 = -21
Adding 9 to both sides gives:
4x = -12
Dividing both sides by 4 gives:
x = -3
So, the boundary line is x = -3, which is a vertical line passing through -3 on the x-axis.
To graph the inequality on a number line, we first locate -3 as a point on the number line. Then, since the inequality is "greater than or equal to," we shade everything to the right of -3 on the number line.
Below is a rough sketch of the number line:
-∞ -5 -4 -3 -2 -1 +∞
-------------------------------------------->
|_______________________|
The shaded region represents the solution to the inequality 4x - 9 ≥ -21.