A one-variable inequality describes a range of values, not one exact solution. When the question asks which number works, graph the inequality in Desmos and find the shaded side of its boundary. A strict inequality leaves the boundary out. If you solve by hand instead, remember that dividing both sides by a negative reverses the inequality sign.
Hints
- Hint 1
A solution region is the shaded part of a graph where the inequality is true. Enter the inequality as written in Desmos. Which side of the boundary does Desmos shade?
- Hint 2
A strict inequality uses or , so a value that makes both sides equal cannot work. Look for a listed value inside the shading, not on its edge.
Step-by-step
Approach 1: Graph the allowed values
Step 1Find the shaded side
Type into Desmos. It shades the area left of and draws a dashed boundary there. The shading shows the values that work; the dashed boundary is excluded. That matches the strict sign: equality isn't enough.
- Step 2
Pick a value in the shading
Of the listed values, only is less than . Type to mark it; Desmos plots the point in the shaded area. Its -coordinate satisfies the inequality, so works. Choice D.
Approach 2: See why the sign points left
Step 1Remove the constant
Subtract from both sides to get the term alone. Subtracting the same amount keeps the inequality sign pointing the same way:
- Step 2
Reverse the sign when dividing
Divide both sides by . Dividing by a negative reverses the order of the numbers, so becomes :
- Step 3
Choose from the allowed range
The symbol means must be below . Of the listed values, only is below it, so satisfies the inequality. Choice D.