Splash Screen. Over Chapter 4 5-Minute Check 1 Write the equation for the line that has slope 3 and y-intercept –5? Write the equation of the line that.

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Solving Addition and Subtraction Inequalities

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Presentation transcript:

Splash Screen

Over Chapter 4 5-Minute Check 1 Write the equation for the line that has slope 3 and y-intercept –5? Write the equation of the line that passes through (3, 5) and (–2, 5). Write the equation of the line that passes through (6, –1) and is perpendicular to the graph of y = x – __

Over Chapter 4 5-Minute Check 2 y = 5 y = 3x – 5 y = – 4x __

Then/Now Linear Inequalities Essential Questions: How are symbols useful in mathematics? What mathematical symbols do you know? Chapter 5

Learning Goal: To solve linear inequalities by using addition and subtraction Lesson 5-1 Solving Inequalities by Addition and Subtraction

Concept

Example 1 Solve by Adding Solve c – 12 > 65. Check your solution. c – 12> 65Original inequality c – > Add 12 to each side. c> 77Simplify. Answer: The solution is the set {all numbers greater than 77}. CheckTo check, substitute 77, a number less than 77, and a number greater than 77.

Example 1 Solve k – 4 < 10.

Vocabulary set-builder notation- more concise way to write the solution set. Graph the solution set on a number line. If the endpoint is not included, use a circle. If the endpoint is included, use a dot.

Concept

Example 2 Solve the inequality x + 23 < 14. A {x|x < –9} B {x|x < 37} C {x|x > –9} D {x|x > 39} Read the Test Item You need to find the solution to the inequality.

Example 2 Solve the inequality m – 4  –8.

Example 3 Variables on Each Side Solve 12n – 4 ≤ 13n. Graph the solution. Answer: Since –4 ≤ n is the same as n ≥ –4, the solution set is {n | n ≥ –4}. 12n – 4 ≤ 13nOriginal inequality 12n – 4 – 12n ≤ 13n – 12nSubtract 12n from each side. –4≤ nSimplify.

Example 3 Solve 3p – 6 ≥ 4p. Graph the solution.

Concept

Example 4 Use an Inequality to Solve a Problem ENTERTAINMENT Panya wants to buy season passes to two theme parks. If one season pass costs $54.99 and Panya has $100 to spend on both passes, the second season pass must cost no more than what amount?

Example x  100Original inequality x –  100 – 54.99Subtract from each side. x  45.01Simplify. Answer: The second season pass must cost no more than $ Use an Inequality to Solve a Problem

Example 4 A.$8.15 B.$8.45 C.$9.30 D.$7.85 BREAKFAST Jeremiah is taking two of his friends out for pancakes. If he spends $17.55 on their meals and has $26 to spend in total, Jeremiah’s pancakes must cost no more than what amount?

End of the Lesson