An inequality usually has a range of solutions, even when the question asks for one value. Graph the given inequality in Desmos and look for the shaded side of its boundary. The shaded side contains the solutions. A dashed boundary itself does not count when the comparison uses rather than .
Hints
- Hint 1
An inequality describes all the numbers that make a comparison true. Graph in Desmos. Which side of the dashed line is shaded?
- Hint 2
A strict inequality uses , so a value on the dashed boundary does not count. Which offered value lies inside the shaded region rather than on or outside its edge?
Step-by-step
Approach 1: Read the solution region in Desmos
Step 1Find the allowed values
Type in Desmos. The boundary, where the two sides are equal, is the dashed line at . Desmos shades to its left, so the values that work satisfy . The line is dashed because does not include equality.
- Step 2
Choose a value in the shaded region
Of the offered values, only is less than . It lies in the shaded region, so it satisfies the inequality. Choice D.
Approach 2: Solve by hand to see why the direction changes
Step 1Remove the constant
Subtract from both sides. Subtracting the same number keeps the comparison direction unchanged:
- Step 2
Reverse the sign when dividing
Dividing by a negative number reverses the order of two numbers on a number line. Divide both sides by and reverse to :
- Step 3
Pick a value below the boundary
means must be less than , not equal to it. The offered value meets that condition. Choice D.