Writing Solving Graphing OneStep Inequalities Objective To write
Writing, Solving, & Graphing One-Step Inequalities Objective: To write, graph, and solve one-step inequalities
MCC. EE. 8 Write an inequality of the form x>c or x<c to represent a constraint or real-world or mathematical problem. Recognize that inequalities of the form x>c or x<c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
What strategies can I use to help me understand represent real situations using inequalities? How can I write, interpret and manipulate inequalities?
An inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality. An inequality may have more than one solution. Together, all of the solutions are called the solution set.
Symbol < > Meaning Word Phrases is less than Fewer than, below More than, above ≤ is greater than is less than or equal to ≥ is greater than or equal to At least, no less than At most, no more than
Write an inequality for each situation. C. There are fewer than 10 gallons of gas in the tank. gallons of gas < 10 or x < 10 “fewer than” means less than. D. There are more than 10 yards of fabric left. yards of fabric > 10 or x > 10 “more than” means greater than
Write an inequality for each situation. A. There at least 15 people in the waiting room. number of people ≥ 15 or x ≥ 15 “At least” means greater than or equal to. B. The tram attendant will allow no more than 60 people on the tram. number of people ≤ 60 or x ≤ 60 “No more than” means less than or equal to.
You can graph the solutions of an inequality on a number line. To indicate that solutions include numbers with values less than the point graphed, shade to the left of the point. To show that solutions include numbers greater than the point graphed, shade to the right of the point.
If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle. This open circle shows that 5 is not a solution. a>5 If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle. This closed circle shows that 3 is a solution. b≤ 3
Symbols Review Open Circle • The number is not included in the solution. Closed Circle • The number is included in the solution.
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