A linear inequality asks for a range of values, not one number. The two sides are equal at a boundary, so a Desmos regression can find that cutoff. Then get alone to determine which side works. Subtracting never flips the inequality sign; dividing flips it only when the divisor is negative. A strict sign leaves out the boundary.
Hints
- Hint 1
The boundary is where the two sides are equal. In Desmos, replace with and with to find that cutoff. The cutoff alone doesn't tell you which side works.
- Hint 2
Move the -terms together by subtracting from both sides. Subtracting the same amount from each side keeps the inequality pointed the same way.
- Hint 3
After you get the -term alone, divide by its positive coefficient. Does a positive divisor change the inequality sign? Does the strict include the cutoff?
Step-by-step
Find the boundary, then isolate
Step 1Find the boundary in Desmos
The two sides meet at the boundary. Type in Desmos: tells Desmos to solve for the value, and asks it to make the sides equal. Under PARAMETERS, Desmos shows . That's the cutoff, but you still need the inequality to tell you which side works.
- Step 2
Bring the -terms together
Subtract from both sides. Subtraction preserves the inequality's direction:
- Step 3
Remove the constant
Add to both sides to remove . Addition also preserves the direction:
- Step 4
Read the solution set
Divide both sides by positive , so the sign stays :
Only multiplying or dividing by a negative reverses an inequality. So the solution set is every number less than ; the strict leaves out itself. Choice B.