Wednesday Warm Up Solve and compare solutions with your neighbor. 2x + 5 = -3x – 15 -3x + 4 = -(2x + 7) 3(x + 4) = 2(x – 7) X = -4 X = 11 X = -16

Unit 1 Solving Inequalities

Objectives I can use basic algebra strategies to solve inequalities for missing information I can graph solutions for inequalities on a number line

Solving Inequalities 1.Get the variable terms together on the left side of the equation 2.Move all the numbers to the other side of the equation. 3.Always undo the operation with its opposite

Graphing the Inequalities An open circle indicates the number is excluded from the solution A closed circle indicates the number is included in the solution Draw a number line with at least 3 numbers, plus the direction arrow. Lets do some examples

Open Circles Used when you have the inequality symbols ( ). The open circle means the number being circled is not in the solution. x > 2 Graph: 2 3 1

Closed Circles Closed Circles used when the inequalities are (  or  ). Closed circles mean the number being circles is in the solution set. x  2 Graph: 2 3 1

EXAMPLE 1 Graph simple inequalities a. Graph x < 2. The solutions are all real numbers less than 2. An open dot is used in the graph to indicate 2 is not a solution.

EXAMPLE 1 Graph simple inequalities b. Graph x ≥ – 1. The solutions are all real numbers greater than or equal to – 1. A solid dot is used in the graph to indicate – 1 is a solution.

EXAMPLE 2 Graph compound inequalities a. Graph – 1 < x < 2. The solutions are all real numbers that are greater than – 1 and less than 2.

EXAMPLE 2 Graph compound inequalities b. Graph x ≤ – 2 or x > 1. The solutions are all real numbers that are less than or equal to – 2 or greater than 1.

Ex 1: 6x + 3 > 5x -2 6x + 3 > 5x –2 x + 3 > -2 (subtracted 5x from both sides) x > -5 (subtracted 3 from both sides)

Ex 2: 3 + 2x < 3x x < 3x – x < 9 (subtracted 3x from both sides) -x < 6 ( subtracted 3 from both sides) x > -6 (divided both sides by –1, switched the inequality sign) x > -6

BIG DIFFERENCE If you multiply or divide each side of an inequality by a negative number then the order of the inequality must be switched.

EXAMPLE 4 Solve an inequality with a variable on both sides Solve 5x + 2 > 7x – 4. Then graph the solution. 5x + 2 > 7x – 4 – 2x + 2 > – 4 – 2x > – 6 x < 3 Write original inequality. Subtract 7x from each side. Subtract 2 from each side. Divide each side by – 2 and reverse the inequality. ANSWER The solutions are all real numbers less than 3. The graph is shown below.

Human Inequalities You should have a 3x5 card Either a Number or Variable Both sides of 3x5 card

Word Problems You have $500 to replace your bathroom floor tile. The tile cost $370 and the tile saw costs $40 per hour to rent. Write and solve an inequality to find the possible numbers of hours you can rent the saw and stay under your budget.

Solution: Total money: Tile: Saw Rental: Possible Inequality: Solution: $500 $370 $40 per hour x ≤ 500 x ≤ 3.25 hours

Homework WS 1-2 Inequalities