Solve each equation. 1.5(x – 6) = 402.5b = 2(3b – 8)3.2y + 6y = 15 – 2y + 8 4.4x + 8 > 20 Absolute Value Equations and Inequalities Solve each inequality.

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Presentation transcript:

Solve each equation. 1.5(x – 6) = 402.5b = 2(3b – 8)3.2y + 6y = 15 – 2y x + 8 > 20 Absolute Value Equations and Inequalities Solve each inequality. 6.4(t – 1) < 3t a – 2 a + 6 > –

1.5(x – 6)=402.5b=2(3b – 8) = 5b=6b – 16 x – 6 = 8–b = –16 x = 14b = 16 Solutions Absolute Value Equations and Inequalities 5(x – 6) a – 2a (t – 1)<3t + 5 3a – a6 + 24t – 4<3t + 5 2a84t – 3t<5 + 4 a4t<9 3.2y + 6y=15 – 2y x + 8>20 2y + 6y + 2y= x>12 10y=23x>3 y=2.3 > – > – > – > –

1.1 Points, Lines, Planes, and Angles

Vocabulary… Point – A location in space Line – A geometric shape made up of at least two points and had no width or thickness Collinear – Points on the same line. Plane – A flat surface made up of at least three noncollinear points, or a line and one non-collinear point. It has an infinite length and width but no depth. Undefined Term – Any term that has been defined using examples and descriptions instead of a mathematical proof. Space – A boundless three dimensional set of all points. It can contain lines and planes.

POINT P Drawn: as a dot Named by: a capital letter Facts: has neither shape nor size

LINE Drawn: with an arrowhead at each end Named by: the letters representing two points on the line OR a lowercase script letter Fact: there is exactly one line through any two points Words/Symbols: line n, line AB, or AB, line BA or BA

PLANE Drawn: as a shaded, slanted, 4-sided figure Named by: a capital script letter OR by names three noncollinear points Fact: There is exactly one plane through any three noncollinear points. Words/Symbols: plane T, plane XYZ, plane XZY, plane YXZ, plane YZX, plane ZXY, plane ZYX X Y Z

Example 1 Use the figure to name each of the following. a.A line containing point K b.A plane containing point L. J K L M B a

EX 2. Visualization… Name the geometric shape modeled by each object. a.The long hand on a clock b.A 10 x 12 patio c.The location where the corner of the driveway meets the road

Example 3 Draw and label a figure for each relationship. Plane R containing lines AB and DE intersect at point P. Add point C on plane R so that it is not collinear with AB or DE.

Example 4a S B C D E A How many planes appear in this figure?

Example 4b S B C D E A Name three points that ARE collinear.

Example 4c S B C D E A Are points A, B, C and D coplanar?

Example 4d S B C D E A At what point do DB and CA intersect?

You try… Page 9 #’s 1-12

Homework… Page 9 #’s 13 – 20