Ch. 4 Block 1

Absolute Value

100

|3x+1| = 52

x = 17 or -17 and 2/3

200

|x³|=125

x = 5 or -5

300

|4x+2|= -14

not possible

400

7 + |.5x-4| *(-6) = -17

x = 16 and 0 

500

4|x - 3| = 16

x = 7 and -1

Elimination

100

2x +24 = 4y

y = -x +12

x = 4 and y = 8

200

4x + - 2y = 40

-6x+3y = -18

no solution 

300

-2x+3y = 18

4y + 2x = 10 

y = 4 and x = -3

400

7x + 4y = 22

5x + 2y = 14

x = -2 and y = 12

500

Josh the zookeeper has to look over the giraffes and elephants.  the number of elephants is 17 more than 5 times the number of giraffes.  Food costs $5 per pound for elephants and $4 per pound for giraffes.  Josh spent $927 on food in total.  Write a system of equations to represent this situation.  

e = 5g+17

5e + 4g = 927

Exponents

100

(x⁷ * x²⁰)/(x³ * x⁴)

x²⁰

200

(28x³)⁴

614656x¹²

300

Beans and Doug went to the Somerville math zoo.  Once they got there, they entered a drumstick eating contest.  Doug ate 26 times the number of drumsticks that beans ate.  In total they spent $228 on drumsticks.  How much did each person spend on drumsticks?  Write a system to represent this.  You do not need to solve.  

26b = d

b + d = 228 

400

(5*5*5x⁵)²

15625x¹⁰

500

(16x¹⁰y^-6z⁸)/(8x¹⁵y⁷z^-7) 

(2z¹⁵)/x⁵y¹³

Substitution/Equal Values

100

x + 2y = 4

y = 3x- 5

x =2 and y = 1

200

5-x = 3y

x = 2y

x = 2 and y = 1

300

2x- y = 12

x - y = 3

x = 9 and y = 6

400

x = -8y + 6

x = 2(5x+3)+5

x = 148/18 and y = -5/18

500

y = -1/12(x) +26

y = 3/4(x) +4

x = 26 and 2/5

y = 23 and 5/6

Linear Growth

100

Liam earns 50 cents per day and has $68.  What is the linear equation that matches this situation. 

y = .5x + 68

200

What is the y intercept of a line with a slope of 5/8 and a point of (16,10) ?

y = 0

300

x²/4 = 4 solve for x

x = 4 

400

513 x - 171y = 1539

solve for x 

x = 1/3 y + 3

500

find the equation of a line that passes through (10, 37) and (35, 62) 

 y = x + 27