Absolute Value Equations
|r/5|=1
r=5 or r=-5
|k-5|<=6
-1<=k<=11
The length of a basketball court can vary from 84 ft to 94 feet, inclusive. Write an inequality that would represent this.
84<=x<=94
6(8k+1)+1=-137
x=-3
-2<x+2<=8
-4<x<=6
Solve for x
3x-19c=36+4c
x=12+(23c)/3
|2+3n|+3=5
n=0 or n=-4/3
|-4p-2|/4>5
p<-11/2 or p>9/2
Matt is buying rubber ducks. He has to pay a shipping fee of $9.99 and each rubber duck costs $5.99. Matt only has $80 to spend. How many rubber ducks can he purchase?
Matt can purchase at most 11 rubber ducks
4(3r+8)-(1+3r)>=49
r>=2
5k-7>13 or6k+10<=-32
k>4 ork<=-7
Solve for h
A=1/2bh
h=(2A)/b
5|8r+7|-5=-5
r=-7/8
-4-7|-b+3|>= -11
b>=2, b<=-4
Find three consecutive even integers such that three times the second equals six more than the sum of the first and the third.
The integers are 4,6 and 8
5p-7(8+7p)<=3(-p-5)
p>=-1
-8-2y>12 or 10-10y<-80
y<-10 or y>9
Solve for h
S=2pih+r^2
h=(S-r^2)/(2pi)
4-7|-5k-8|=-10
k=-2 or k=-6/5
-3|-7+6b|-6> -93
-11/3<b<6
Bill scored a 75 on his first test and an 80 on his second test. What will he have to score on his third test to obtain an average of at least 80?
He would have to score at least an 85 on his third test.
(3x)/2+(5x)/3-(13x)/6-2/3=5/6
x=3/2
4-8w<=-2w-2 and -2w-2<=8-4w
w>=1 and w<=5
Solve for x
(3zy)/4-4x=(zy)/6
x=(48z)/(7y)
|3x-4|=5x-8
x=2
2|x-4|-3<-8
No Solution
Bruce is 4 years younger than Hector. Twenty years ago, Hector’s age was 13 years more than half the age of Bruce. How old are they now?
Bruce is 38 and Hector is 42.
− 1 /4(4x − 24) + 12 = 3 /7 (7x − 77) + 11
x=10
3x<4-5x<5+3x
x<1/2 andx > -1/8
Solve for w
x(y-w)=5+2xy
w=-5/x-y