Chapter 2 Equations and Inequalities

HW Quiz #1.6-10 Wednesday, April 19, 2017 Yellow: 1, 3, 5 White: 2, 4

No HW Quiz #1.6-10 Pass Your HW to the front!

2.1 More on Solving Equations

Objective: Solve equations containing fractions or decimals. When an equation contains fractions or decimals, we can use the multiplication property to eliminate them. The process is called clearing the equation of fractions or decimals.

Solving an Equation with Decimals Solve the equation by clearing it of all decimals first.

Solve the equation by clearing it of all fractions or decimals first.

Solving an Equation with Zero Products Objective: Use the principle of zero products to solve equations. Solving an Equation with Zero Products

Solving an Equation with Zero Products

Solving an Equation with Zero Products Solve the equation using the zero products property.

Solving an Equation Solve the equation

Solving an Equation Solve the equation

2.2 Using Equations

Objective: Solve problems by translating to equations.

Objective: Solve problems by translating to equations. A 23-ft cable is cut into two pieces, one three times as long as the other. How long are the pieces?

Herman is doing an experiment that calls for a 40% solution of copper sulfate. He has a 60ml of a solution that is 25% copper sulfate. How many milliliters of a 70% solution should Herman add to obtain the required 40% solution?

Two cars leave the 7-11 at the same time going in the same direction Two cars leave the 7-11 at the same time going in the same direction. One car is going 45 mph and the other car is going 58 mph. In 2.5 hours how far apart are they?

A popular music CD was discounted 25% to $8. 42 A popular music CD was discounted 25% to $8.42. What was the original price?

Write an equation and use it to solve the following F A tank at a marine exhibit contains 2000 gallons of sea water. The sea water is 7.5% salt. How many gallons, to the nearest gallon, of fresh water must be added to the tank so that the mixture contains only 7% salt?

HW #2.1-2 Pg 64 15-41 Odd, 42-46 Pg 70 19-27 Odd

HW Quiz #2.1-2 Wednesday, April 19, 2017 Pg 64 41 Pg 64 44 Pg 70 25 Pg 70 27 Pg 64 39 Pg 64 42 Pg 70 21

2.3 Solving Formulas

Solving a Formula for a specific variable Objective: Solve a formula for a specified letter. A formula is a rule for doing a specific calculation. Solving a Formula for a specific variable

Solving a Formula for a specific variable

Solving a Formula for a specific variable

Solving a Formula for a specific variable

2.4 Solving Inequalities

Objective: Determine if a number is a solution of an inequality and graph the solution set. If a number occurs to the left of another on the number line, the first number is less than the second, and the second is greater than the first.

Determine whether the given number is a solution of the inequality. Objective: Determine if a number is a solution of an inequality and graph the solution set. Determine whether the given number is a solution of the inequality. x + 3 < 6;5 3 - x < 2; 4 3x + 2  4x - 3; 5

Determine whether the given number is a solution of the inequality. C: x - 3 < 6;5 D: 3x + 2  4x - 3; 6

Objective: Solve and graph inequalities using the addition property.

Solving an Inequality

Objective: Solve and graph inequalities using the multiplication property.

Solving an Inequality

Solving an Inequality

E F

Solving an Inequality

Solving an Inequality

HW #2.3-4 Pg 72 17-23 Odd, 25-31 Pg 77 19-27 Odd, 28-38

HW Quiz #2.3-4 Wednesday, April 19, 2017 Pg 72 26 Pg 72 28 Pg 77 30 Pg 77 34 Pg 72 30 Pg 77 32 Pg 77 36

2.5 Using Inequalities

Suppose that a machinist is manufacturing boxes of various sizes with rectangular bases. The length of a base must exceed the width by at least 3 cm, but the base perimeter cannot exceed 24 cm. What widths are possible?

2.6 Compound Inequalities

Objective: Solve compound inequalities. A compound inequality is two simple inequalities joined by “and” or “or.” Statements involving the word “or” are called disjunctions. A disjunction is true when at least one of the statements is true Statements involving the word “and” are called conjunctions. For a conjunction to be true all individual statements must be true

Conjunctions In mathematics, conjunction is called intersection and is symbolized by the symbol: 

Disjunctions In mathematics, disjunction is called union and is symbolized by the symbol: 

Solve the following inequalities Solve the following inequalities. Graph your solution on a number line and write them in interval notation.

Write and solve a compound inequality that is the conjunction of two disjunctions. Write an inequality that has no solution and show it has no solution. Write an inequality whose solutions are all real numbers and show why the solutions are all real numbers.

HW #2.5-6 Pg 81 10-18 Pg 85-86 1-31 Odd, 33-45

HW Quiz #2.5-6 Wednesday, April 19, 2017 Solve Write answer in interval notation -2 < 3x – 4 < 8 -2 < 3x – 4 or 3x – 4 ≤ 8 -4 < 3x – 4 < 8 -4 < 3x – 4 or 3x – 4 ≤ 8 Row 1, 3, 5 Row 2, 4

2.7 Absolute Value

|2| = |-2| = 2

Objective: Simplify absolute value expressions.

Objective: Find the distance between two points using absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

Objective: Solve and graph equations and inequalities involving absolute value.

HW #2.7 Pg 91 1-37 Odd, 38-51

HW Quiz #2.7 Wednesday, April 19, 2017 Solve |2x – 3| > 5 |2x – 3| < 11 |3x – 2| > 6 |3x – 2| < 10 Row 1, 3, 5 Row 2, 4

2-8 Proofs in Solving Equations

Test 1-2 Part 1-5Questions 2-proofs 1-Closure Any Proof in the HW Any Proof I did in class 1-Closure 2 questions with no numbers

Conditional Statements Objective: Prove conditional statements. Conditional Statements Antecedent Hypothesis Consequence Conclusion To prove a conditional statement you assume the Hypothesis and Show the conclusion must also be true.

Use a two column proof or narrative proof

Objective: Write and prove the converse of a conditional statement. Converse of the Conditional Statement To prove a the converse of a conditional statement you assume the Conclusion and Show the Hypothesis must also be true.

Objective: Solve equations and inequalities by proving a statement and its converse. Biconditional

HW #2.8 Pg 96-97 1-21 Odd, 23-32

Test Review Topics Simplify – Order of Operations Solve Equations Exponents – Multiply/Divide – Negative Exponents Word Problem Compound Inequalities – Interval Notation Absolute Value Sign Charts Solve for a Variable Factoring – to solve quadratics

A suitcase of money contains b hundred dollar bills A suitcase of money contains b hundred dollar bills. After the bills are distributed evenly among g federal agents, 8 hundred dollars bills are left over. In terms of b and g, how many hundred dollar bills did each agent get?

If a Citation Jet travels at an average speed of x miles per hour, how many hours would it take the Citation to travel 800 miles?

HW R1-2 Study Hard

Find the area of an equilateral triangle