For a system of inequalities, a point must satisfy every condition. Graph both inequalities in Desmos, then look at the shared shading to find the possible -coordinates. Check whether the highest apparent point is included: a solid sloping line can meet a dashed vertical line at a point the system excludes.
Hints
- Hint 1
Each inequality shades the points that satisfy it. Look at the overlap, where both conditions hold. Which edge of that region controls how high can be?
- Hint 2
The strict inequality excludes the line . Find the sloping line's height there, then ask what happens to that height as moves right.
- Hint 3
Finding an upper limit isn't quite enough: the answer must include every lower height that works. Does the overlapping shading reach every height below its top?
Step-by-step
Graph the overlap and check its top edge
Step 1Graph both conditions
Type and into Desmos. The overlap, where both shadings cover a point, is to the right of the dashed line and on or below the solid sloping line.
- Step 2
Find the height at the excluded edge
Type to find the sloping line's height at . Desmos prints , so the lines meet at . That point is excluded because must be greater than .
- Step 3
Determine whether any higher point works
The slope is the line's change in height when increases by . Here it's , so moving right of puts the sloping line below . Since must be on or below that line, the apparent top height is unreachable because is excluded.
- Step 4
Include every height below the top
For any height below , you can move a small enough distance right of that the sloping line is still above that height. The shading includes the points below the line, so every such height occurs. The possible -coordinates are . Choice A.