Inequalities Review Agenda –Review Inequalities –Begin Homework P 570 (2-20 evens) P 574 (5-9 & odds) P 576 (20-24 evens) Study for Practice CST which starts tomorrow!

Solve 8 d – 2. Graph and check your solution. > d – 2 + 2Add 2 to each side. > 10 d, or d 10Simplify. >< Check: 8 = d – 2Check the computation – 2Substitute 10 for d. 8 = 8 8 ≥ d – 2 Check the direction of the inequality. 8 ≥ 9 – 2 Substitute 9 for d. 8 ≥ 7 Solving Inequalities Using Addition and Subtraction Quick Check

Solve c + 4 > 7. Graph the solution. c + 4 – 4 > 7 – 4Subtract 4 from each side. c > 3Simplify. Solving Inequalities Using Addition and Subtraction Quick Check

Solve and graph the inequalities. 1) 2)

1) 2)

Solve 8z – 6 < 3z z – 6 – 3z < 3z + 12 – 3zSubtract 3z from each side. 5z – 6 < 12Combine like terms. 5z – < Add 6 to each side. 5z < 18Simplify. < Divide each side by 5. 5z55z z < 3Simplify Solving Multi-Step Inequalities Quick Check

Solve 5(–3 + d) 3(3d – 2). < –15 – 4d + 15 –6 + 15Add 15 to each side. < –4d 9Simplify. < –15 + 5d – 9d 9d – 6 – 9dSubtract 9d from each side. < –15 – 4d –6Combine like terms. < –15 + 5d 9d – 6Use the Distributive Property. < d –2Simplify. > 1414 Divide each side by –4. Reverse the inequality symbol. –4d –4 9 –4 > Solving Multi-Step Inequalities Quick Check

Objective - To graph linear inequalities in the coordinate plane. Number LineCoordinate Plane y x x = 3

Number LineCoordinate Plane y x y = -2

Boundary Line Test a Point False! y x If y = mx + b, soliddashed shade up shade down

Boundary Line Dashed line Shade up y x If y = mx + b,

y x Solid line Shade up If y = mx + b,

y x Dashed line Shade down If y = mx + b,

If you are given a point and a slope, you write the equation of the line in point slope form by plugging in the slope and the x and y from the point into: y – y 1 = m (x – x 1 ) y 1 is the y from the point. m is the slope. x 1 is the x from the point. Point-Slope Equation

If you are asked to write the equation in slope- intercept form, first write the equation in point- slope form. y – y 1 = m (x – x 1 ) y 1 is the y from the point. m is the slope. x 1 is the x from the point. Then distribute the “m” to the x and the x 1 Then get the y alone on the left.

First write the equation in point- slope form. y – y 1 = m (x – x 1 ) y 1 is the y from the point. m is the slope. x 1 is the x from the point. Then distribute the “m” to the x and the x 1 Then get the y alone on the left. m = ¼ (3,-2) y – -2 = ¼ (x – 3) y – -2 = ¼ x – ¾ y = ¼ x – ¾ -2y = ¼ x –2 ¾

If you are given two points and no slope, you find the slope using the slope formula : y 2 – y 1 x 2 – x 1 Then write the equation of the line in point slope form by plugging in the slope and the x and y from either one of the points into: y – y 1 = m (x – x 1 ) y 1 is the y from the point. m is the slope. x 1 is the x from the point.