Chapter 5 Notes Algebra Concepts. Section 5-1: Solving Linear Inequalities by Addition and...

Chapter 5 Notes

Algebra Concepts

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Inequality –

Addition Property of InequalitiesWords:

Symbols:

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Inequality – A mathematical sentence that contains < , > , < , or >

Addition Property of InequalitiesWords: Any number is allowed to be added to both sides of a true inequality

Symbols: If a > b, then a + c > b + cIf a < b, then a + c < b + c

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Graphing inequalities on a number line:1) Put a circle on the _____________ point2) Fill the circle in if the sign is _______ or _______3) Leave the circle open if the sign is _____ or ____4) Shade the left side if the variable is

____________ to the number5) Shade the right side if the variable is

____________ to the numberEx) Graph x < -9 Ex) Graph 4 < x

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Solve the following inequalities and graph the solution set on a number line.1) x – 12 > 8 2) 22 > x – 8 3) x – 14 < -19

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Subtraction Property of InequalitiesWords:

Symbols:

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Subtraction Property of InequalitiesWords: Any number is allowed to be subtracted from both sides of a true inequality

Symbols: If a > b, then a – c > b – cIf a < b, then a – c < b – c

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Solve the following inequalities and graph the solution set on a number line.1) x + 19 > 56 2) 18 > x + 8 3) 22 + x < 5

Section 5-1: Solving Linear Inequalities by Addition and Subtraction

Solve the following inequalities and graph the solution set on a number line.1) 3x + 6 < 4x 2) 10x < 9n – 1

Section 5-2: Solving Inequalities by Multiplication and Division

Multiplication Property of Inequalities: Part 1Words:

Symbols:

Section 5-2: Solving Inequalities by Multiplication and Division

Multiplication Property of Inequalities: Part 1Words: Any positive number is allowed to be multiplied to both sides of an inequality

Symbols (c > 0):If a > b, then ac > bcIf a < b, then ac < bc

Section 5-2: Solving Inequalities by Multiplication and Division

Multiplication Property of Inequalities: Part 2Words:

Symbols:

Section 5-2: Solving Inequalities by Multiplication and Division

Multiplication Property of Inequalities: Part 2Words: Any negative number is allowed to be multiplied to both sides of an inequality, as long as the sign gets flipped!

Symbols (c < 0):If a > b, then ac < bcIf a < b, then ac > bc

Section 5-2: Solving Inequalities by Multiplication and Division

Solve1) 2)

3) 4)

Section 5-2: Solving Inequalities by Multiplication and Division

Division Property of Inequalities: Part 1Words: Any positive number is allowed to be divided to both sides of an inequality

Symbols (c > 0): If a > b, then

If a < b, then

Section 5-2: Solving Inequalities by Multiplication and Division

Division Property of Inequalities: Part 2Words: Any negative number is allowed to be divided to both sides of an inequality, as long as the sign gets flipped!Symbols (c < 0): If a > b, then

If a < b, then

Section 5-2: Solving Inequalities by Multiplication and Division

Solve and graph the solution set1) 4x > 16 2) -7x < 147

3) -15 < 5x 4) -20 > -10x

Section 5-3: Solving Multi-Step Inequalities

Solve the following multi-step inequalities. Graph the solution set.1) -11x – 13 > 42 2) 15 + 2x < 31

3) 23 > 10 – 2x

Section 5-3: Solving Multi-Step Inequalities

Solve the following multi-step inequalities. Graph the solution set.1) 4(3x – 5) + 7 > 8x + 3

2) 2(x + 6) > -3(8 – x)

Section 5-3: Solving Multi-Step Inequalities

Translate the verbal phrase into an expression and solveFive minus 6 times a number n is more than four times the number plus 45

Section 5-3: Solving Multi-Step Inequalities, SPECIAL SOLUTIONS

Solve the following inequalities. Indicate if there are no solutions or all real number solutions.1) 9x – 5(x – 5) < 4(x – 3) 2) 3(4x + 6) < 42 + 6(2x – 4)

Section 5-6: Graphing Linear Inequalities

Linear Equations vs.• Plot any 2 points• Draw a solid line through

the 2 points

Linear Inequalities• Put in slope-int form first• Plot any two points• Determine whether to

connect the points with a solid OR dashed line

• Shade ONE side of the line– You must determine which

side– You shade the solution set!

Section 5-6: Graphing Linear Inequalities

Steps for graphing linear inequalities:1) Plot 2 points on the line2) If the symbol is < or >

connect with a dashed line3) If the symbol is < or >,

connect with a solid line4) Shade above the line for

y > mx + b (or >)5) Shade below the line for

y < mx + b (or <)

Ex. Graph y < 2x – 4

Section 5-6: Graphing Linear Inequalities

Graph the following linear inequalitiesEx) Ex) y < x – 1

Section 5-6: Graphing Linear Inequalities

Graph the following linear inequalitiesEx) 3x – y < 2 Ex) x + 5y < 10