Solve each equation.

1. 5(x – 6) = 40 2. 5b = 2(3b – 8) 3. 2y + 6y = 15 – 2y + 8

4. 4x + 8 > 20

Absolute Value Equations and Inequalities

Solve each inequality.

6. 4(t – 1) < 3t + 55. 3a – 2 a + 6>–

1. 5(x – 6) = 40 2. 5b = 2(3b – 8)

= 5b = 6b – 16

x – 6 = 8 –b = –16x = 14 b = 16

Solutions

Absolute Value Equations and Inequalities

5(x – 6)5

405

5. 3a – 2 a + 6 6. 4(t – 1) < 3t + 53a – a 6 + 2 4t – 4 < 3t + 5

2a 8 4t – 3t < 5 + 4a 4 t < 9

3. 2y + 6y = 15 – 2y + 8 4. 4x + 8 > 202y + 6y + 2y = 15 + 8 4x > 12

10y = 23 x > 3y = 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 non-

collinear 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

• PDrawn: as a dotNamed by: a capital letterFacts: has neither shape nor size

LINE

Drawn: with an arrowhead at each endNamed 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 figureNamed by: a capital script letter OR by

names three noncollinear pointsFact: 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.

JK

L

M

B

a

EX 2. Visualization…

• Name the geometric shape modeled by each object.

a. The long hand on a clockb. A 10 x 12 patioc. 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