Basic Equations
Solve for x:
7x+6=5x+36
x=15
A cell phone company charges $50 for 1500 text messages. Each additional text message over that amount costs 20 cents each. If Blake's bill is $80, then how many total text messages did he send?
1650 text messages
Solve for n and put your answer in interval notation:
-6>5n+5+4
(-inf,-3)
Solve for x:
|3x|=9
3 and -3
What is the equation of this variation statement?
"y varies inversely as x"
y=k/x
Solve for x:
x2+4=68
x=8,-8
A pasture is twice as long as it is wide. It's area is 115,200 square feet. How wide is the pasture?
240 feet
Solve for x and put answer in interval notation:
5x+6<13
(Bold inequality means or equal to)
(-inf,7/5)
Solve for x:
|-4+5x|=16
-12/5 and 4
What is the equation of this variation statement?
"A varies directly as m and inversely as n."
A=km/n
Solve for x:
1/2(x+3)2=1
x=-3+sqrt(2), -3-sqrt(2)
Two cyclists, 80 miles apart, start riding toward each other at the same time. One cycles three times as fast as the other. If they meet 2 hours later, at what average speed is each cyclist traveling?
Slower cyclist: 10 mph; faster cyclist: 30 mph
Solve for x and put your answer in interval notation:
9-3x>-(1+5x)
[-5,inf)
Solve for x:
3|x+2|=15
-7 and 3
Suppose V is directly proportional to W. If V=18 when W=2, find k.
k=9
Solve for k:
EG=ktm
k=EG/tm
Phyllis invested $12,000, a portion earning a simple interest rate of 4.5% per year and the rest earning a rate of 4% per year. After 1 year the total interest earned on these investments was $525. How much money did she invest at each rate?
$9000 at 4.5% and $3000 at 4%
Solve for x and put your answer in interval notation:
8<1-3x<13
(Bold inequality means or equal to)
(-4,-7/3]
Solve for x and put in interval notation:
|x+2|<7
(-9,5)
Suppose J is jointly proportional to the squares of h and g. If J=1800 when h=4 and g=6, find k.
k=1800/576 or 25/8
Solve for b1:
A=1/2h(b1+b2)
b1=2A/h -b2
A bottle contains 750 mL of fruit punch with a concentration of 50% real fruit juice. Jill drinks 100 mL of the punch and then refills the bottle with an equal amount of a cheaper, weaker brand of punch. If the concentration of the juice in the bottle is now reduced to 48%, what was the concentration of the punch that Jill added?
35%
Solve for x and put your answer in interval notation:
2|x|+8>16
(Bold inequality means or equal to)
(-inf,-4]U[4,inf)
Solve for x and put in interval notation:
4|x+3|+3<8
(Bold inequality means or equal to)
[-17/4,-7/4]
Suppose y varies directly as x and indirectly as z. If y=2 when x=5 and z=10, find y when x=3/4 and z=5.
y=3/5