Solving Linear Inequalities in Word Problems: Sesame Seeds

Published on March 13, 2026

Word-Problem

This problem requires setting up and solving a one-variable linear inequality based on a real-world constraint (total resources) and interpreting the solution graphically, including contextual bounds.

Question

Answer

Here is the step-by-step solution to the problem.

1. Set up the inequality

The problem states:

Kenji has 21 teaspoons of sesame seeds in total.
He uses 9 teaspoons for the loaf of bread.
He is baking 6 bagels.
Let be the number of teaspoons of sesame seeds on each bagel.

The total amount of sesame seeds used must be less than or equal to the amount he has (21 teaspoons).
Total seeds used = (Seeds for bread) + (Seeds for 6 bagels)
Total seeds used =

The inequality is:

The problem confirms this setup: “Solve the inequality

.”

2. Solve the inequality

We need to solve

for

Step 2.1: Subtract 9 from both sides of the inequality.

Step 2.2: Divide both sides by 6. Since 6 is a positive number, the inequality sign remains the same.

The solution to the inequality is

. This matches the provided entry field:

3. Contextual Constraint

Since

represents the amount of sesame seeds used per bagel, it cannot be negative in this physical context. Therefore, we must also have

Combining the mathematical solution with the physical constraint, the actual range for

is:

4. Determine the correct graph

We need to find the graph that represents

The inequality means we shade to the left of 2, including 2 (represented by a closed/solid dot at 2).
The constraint means we shade to the right of 0, including 0 (represented by a closed/solid dot at 0).

The correct graph must show a solid line segment connecting a solid dot at

and a solid dot at

Let’s examine the options provided:

Solid dots at 0 and 1, shading between them. (Incorrect)
Solid dots at 0 and 2, shading between them. (This matches )
Open circle at 0, closed circle at 2, shading between them. (Incorrect, excludes 0)
Closed circle at 2, shading to the left, extending infinitely. (This matches only , ignoring the physical constraint )

Although the initial algebraic solution is

, the context of the problem (amount of seeds) implies that the number of seeds cannot be negative, so

. Therefore, the graph representing the possible amounts of seeds Kenji can use must show the closed interval

The graph in the second row, right side (or the bottom-left graph in the full set of four, depending on layout presentation, but specifically the one showing shading between 0 and 2 with solid endpoints) best represents the physical situation

. Looking closely at the provided image crops:

The second graph in the left column shows solid points at 0 and 2, with the line segment between them shaded. This represents .

The second graph in the first row of options (from top left) shows open circles at 0 and 2, shading between them.
The bottom right graph shows a closed point at 2 and shading leftwards.
The bottom left graph shows a closed point at 2 and shading between 0 and 2 (inclusive).

The correct representation for

is the graph showing a solid segment between

and

, inclusive of both endpoints. This corresponds to the second graph in the left column.

Final Answer Summary:

Solve the inequality :
Apply context constraint ():
Select the graph: The graph representing is the one with closed dots at 0 and 2, with the segment between them shaded. This is the second graph from the top on the left side.

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