Let x be any real number. Write and graph: x is less than 25. Label the endpoint and shade the solution ray.
x < 25; open circle at 25, shade left
“less than” means <; exclude the endpoint.
Day 098Writing and Graphing Inequalities
Standards 6.EE.B.8
LEARNING TARGET
I can write and graph a constraint using an inequality.
01 · LEARN
Build the idea
Use > or < for a strict bound and ≥ or ≤ when the endpoint is included. Graph a strict bound with an open circle; use a closed circle for an included endpoint. Shade the direction of all solutions.
Let x be any real number. Write and graph: x is at least 8. Give one included value and explain whether the endpoint is included.
x ≥ 8; closed circle at 8, shade right
“at least” means ≥; include the endpoint. Example solution: 9.
02 · PRACTICE
Your turn
Work in order. Start with the foundations, then build toward explanation and application.
Let x be any real number. Write and graph: x is more than 16. Label the endpoint and shade the solution ray.
Let x be any real number. Write and graph: x is less than 12. Label the endpoint and shade the solution ray.
Let x be any real number. Write and graph: x is more than 12. Label the endpoint and shade the solution ray.
Let x be any real number. Write and graph: x is less than 24. Label the endpoint and shade the solution ray.
Let x be any real number. Write and graph: x is more than 15. Label the endpoint and shade the solution ray.
Let x be any real number. Write and graph: x is more than 10. Label the endpoint and shade the solution ray.
Let x be any real number. Write and graph: x is at least 49. Give one included value and explain whether the endpoint is included.
Let x be any real number. Write and graph: x is at least 20. Give one included value and explain whether the endpoint is included.
A museum group must have more than 8 participants. Let p be the participant count. Write an inequality and graph its real-number solution set. State which solutions make sense as participant counts.
A museum group must have at least 42 participants. Let p be the participant count. Write an inequality and graph its real-number solution set. State which solutions make sense as participant counts.
03 · CHECK
Answers and reasoning
Reveal the teacher answer key
- x > 16; open circle at 16, shade right
“more than” means >; exclude the endpoint.
- x < 12; open circle at 12, shade left
“less than” means <; exclude the endpoint.
- x > 12; open circle at 12, shade right
“more than” means >; exclude the endpoint.
- x < 24; open circle at 24, shade left
“less than” means <; exclude the endpoint.
- x > 15; open circle at 15, shade right
“more than” means >; exclude the endpoint.
- x > 10; open circle at 10, shade right
“more than” means >; exclude the endpoint.
- x ≥ 49; closed circle at 49, shade right
“at least” means ≥; include the endpoint. Example solution: 50.
- x ≥ 20; closed circle at 20, shade right
“at least” means ≥; include the endpoint. Example solution: 21.
- p > 8; open circle at 8, shade right; participant counts are whole numbers 9, 10, …
“more than” means >. The real-number ray has infinitely many solutions, but participant counts must be whole numbers.
- p ≥ 42; closed circle at 42, shade right; participant counts are whole numbers 42, 43, …
“at least” means ≥. The real-number ray has infinitely many solutions, but participant counts must be whole numbers.