Advanced Math Study guide

Absolute Value

100

|2x+3|< 5

-4<x<1

200

|2z-9| < 1

4<z<5

300

|3 - 2r| >7

r<-2 or r > 5

400

| -4 + 8k| = 68

k= 9 k=-8

500

-2| -2p - 8 | > -56

-18 < p < 10

Inequality

100

1/2 < c - 3/4

c > 5/4

200

Twelve is at most a number decreased by 7. (simplify)

19 < x

300

2/3n > - 12

n > -18

400

k - 3 < -7 or k + 5 > 8 

k < -4 or k > 3

500

2c - 4 > -6 and 3c + 1 < 13

-1 < c < 4

AND/OR GRAPHS

100

x < -2 or x > 2

200

(Graph) 9|9 + 3x| < 81

             ________________

<--------o---------------------o-------->

             -6                          0

            - 6 < x < 0

300

-5| 4x + 4| > -60

        __________________

<----o-----------------------o-------->

      -4                             2

 -4 < x < 2

400

|-3n + 6| - 9 > 15

<___                                   _____>

<----o--------------------------o------->

       - 6                               10

n < -6 or n > 10

500

-1 + |3 - 2x| < 14

               ________________

<---------o----------------------o-->

             -6                            9

-6 < x < 9

Solving linear equations

100

Use substitution

y = 6x

2x + 3y = -20

(-1,-6)

200

(try to graph?)

3x - y = -2 

3x - y = 0 

NO SOLUTION

300

SOLVE BY SUBSTITUTION

x + 2y = 13

-2x - 3y = -18

(-3, 8)

400

USE ELIMINATION

x - y = 1

x + y = -9

(-4, -5)

500

USE ELIMINATION

4x + y = 23

3x - y = 12

(5,3)

RANDOM

100

SOLVE BY ELIMINATION

2x + 5y = -3

-2x +2y = 6

(6,-3)

200

Find the slope, x- intercept, and y - intercept

1/2 x - 2y = -4

x intercept (-8,0)       y - intercept (0,2)

slope 1/4

300

-4 < -2x - 4 < 12

(Solve the ineqality)

-8< x < 0

400

One number added to three times another number is 24. Five times the first number added to three times the other number is 36. Find the numbers.

First number is 3. Second number is 7.

(3,7)

500

Nick plans to start a dog-treat business. He figures it will cost $20 in operating costs plus $0.50 to product each treat. He plans to sell the treats for $1.50. How many treats does Nick need to sell per week to break even?

20 treats for $30