4-5 solving inequalities using addition and subtraction

4-5 solving inequalities using addition and subtraction Miss battaglia – algebra 1 CP Objective: use addition and subtraction to solve one-step inequalities; use inequalities to model real-world problems.

Warm up • Jackie has $3.50 in quarters and nickels. If she has two more quarters than nickels, how many quarters does Jackie have?

Work with a partner • Define a variable and write an equality for each sign. 1 2 3

Work with a partner • Define a variable and write an equality for each situation. • Persons under 17 are not admitted. • Visibility at the airport is less than 2 miles. • You must be more than 36 in. tall to ride an amusement park ride.

Solution of the inequality • Any value of the variable that makes the inequality true is called a solution of the inequality. • Tell whether each number is a solution of x < 3. • 1 b) – 7.3 c) 9.00 • d) 0 e) 3

Graphing inequalities • x < 4 • An open dot means 5 is not a solution. • x < 4 • A closed dot means 5 is a solution.

graph • x > -1 • x > -1

Equivalent inequalities • Equivalent Inequalities have the same set of solutions. • -4 < 1 • -4 + 2 < 1 + 2 • -2 < 3

Properties of inequality Addition Property of Inequality For any numbers a, b, and c, if a > b then a + c > b + c For any numbers a, b, and c, if a < b then a + c < b + c Subtraction Property of Inequality For any numbers a, b, and c, if a > b then a - c > b - c For any numbers a, b, and c, if a < b then a - c < b - c

Graph the solution on a number line. • x – 3 < 5

Graph the solution on a number line. • w +2> -1

Graph the solution on a number line. • 5.7 > k – 3.1

example • Your bank offers free checking for accounts with a balance of at least $500. Suppose you have a balance of $516.46 and you write the check below. How much must you deposit to avoid being charged a service fee?

homework • Pg182 #1-6, 8, 10, 12, 17,18, 29–35 odd

4-5 solving inequalities using addition and subtraction