Write Inequalities With Fraction Endpoints

Start with Is It a Solution to the Inequality, then move to the graphing sheets. Use the card sorts and Match Inequalities to Graphs as a check or review, since each answer can only go in one place.

Write inequalities for 10 graphs with fraction endpoints, as mixed numbers like 3 2/3. The directions on the page read: Write the inequality shown by each graph. Use x. Count the ticks between two whole numbers to find the endpoint, and write it as a fraction or mixed number in simplest form. The page opens with a worked example, and an answer key is included.

Yes, both. We made it for 8th grade algebra, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Substitute the number for x and work out each side. If the statement is true, the number is a solution. In the opening example, 4(11) − 9 is 35, and 35 ≤ 27 is false, so 11 is not a solution.

Use an open circle for < or >, because the endpoint is not a solution. Use a closed circle for ≤ or ≥, because the endpoint is included. The ray then points toward the rest of the solutions.

Rewrite it with x first. 9 ≥ x means x ≤ 9, so draw a closed circle at 9 and a ray to the left. Several sheets mix both forms so students practice this step.

Read the endpoint, then check the circle and the arrow. An open circle at 9 with a ray to the left is x < 9. When the endpoint sits between labels, count the ticks to find its value first.