For a linear inequality, first find the boundary where the two sides are equal. A Desmos regression can give you that cutoff, but it doesn't tell you which side works. When the number multiplying is negative, increasing makes the left side smaller. Keeping the sign pointed toward larger is the tempting trap.
Hints
- Hint 1
An inequality has a boundary where its two sides are equal. Replace with to find the cutoff. What value makes equal ?
- Hint 2
For a strict inequality, equality at the boundary doesn't count. The multiplying is negative, so making smaller raises . Which side of the boundary works?
Step-by-step
Find the cutoff, then choose a side
Step 1Find the equality boundary
The boundary is where the two sides are equal. Type in Desmos. The tells Desmos to solve for a value rather than graph , and asks it to fit the equality. Under PARAMETERS, Desmos shows . That's the cutoff, not yet the full solution set.
- Step 2
Choose the values that work
In , the coefficient of , the number multiplying it, is . Making smaller makes larger, so the left side rises above . A negative coefficient reverses the direction you might expect from . The strict leaves out the boundary, so the solution set is . Choice C.