Question

kenji is baking a loaf of bread and 6 bagels. he has 21 teaspoons of sesame seeds. he uses 9 teaspoons of sesame seeds on the loaf of bread. he wants to know how many teaspoons of sesame seeds he can use on each bagel. let x be the number of teaspoons of sesame seeds on each bagel. solve the inequality 9 + 6x ≤ 21. x ≤ 2 which graph best represents the teaspoons of sesame seeds kenji can use on each bagel? four number line graphs are shown, with -1, 0, 1, 2 marked. first graph: blue dots at 0, 1, 2. second graph: blue line from 0 to 2, dots at 0 and 2. third graph: blue line from 0 to 2, open circles at 0 and 2. fourth graph: blue line from -1 to 2, dot at 2.

Explanation:

Step1: Analyze the inequality solution

We have the inequality solution \( x \leq 2 \), and since \( x \) represents the number of teaspoons of sesame seeds on each bagel, \( x \) must be non - negative (you can't use a negative amount of sesame seeds). So the domain of \( x \) is \( 0\leq x\leq2 \).

Step2: Analyze the number line graphs

• For a number line graph representing \( 0\leq x\leq2 \), we need a closed circle at \( 0 \) (because \( x = 0 \) is included, as you can use 0 teaspoons of sesame seeds on a bagel) and a closed circle at \( 2 \) (because \( x = 2 \) satisfies \( x\leq2 \)), with the line segment between them shaded.
• The first graph has three separate points, which is not correct.
• The second graph has a line starting from 0 and going to the right, which would represent \( x\geq0 \) without the upper bound of 2, so it's incorrect.
• The third graph has closed circles at 0 and 2 and the line between them shaded, which matches our domain \( 0\leq x\leq2 \).
• The fourth graph has a line going to the left towards - 1 and ending at 2, which represents \( x\leq2 \) including negative values, but \( x \) can't be negative, so it's incorrect.

Answer:

The third graph (the one in the bottom - left among the four graphs, with closed circles at 0 and 2 and the line between them shaded)