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Solving Equations and Inequalities with One Variable
Literal Equations
Systems of Equations
Random
Systems of Inequalities
100
39-8n=-8(3+4n)+3n
n = -3
100
Solve for x: ax+3b=2f
x=(2f-3b)/a
100
Find the solution set to the system of equations ALGEBRAICALLY: y=4x-1 y=-0.5x+8
(2,7)
100
Cab A charges $6 PLUS $0.50 per mile and Cab B charges only $0.80 per mile. When are both cabs the same price?
at 20 miles
100
You want to buy juice and cookies. Juice is $3 and cookies are $4. You must spend less than $35. You need to buy at more than 4 bottles of juice. Write a system of inequalities.
3x+4y<35 x>4
200
7-2x=1-5x+2x
x=-6
200
solve for p: x=10p+35
(x-35)/10
200
Find the solution set to the system of equations ALGEBRAICALLY: 2x+y=4 2x+3y=9
(3/4,5/2)
200
solve for b: c=(b+rm)(1+t)
(c/(1+t))-rm
200
You are selling shirts and hats. Shirts cost $15 and hats are $10. You need to make more than $1200. You know you will sell more than 10 shirts. Write a system of inequalities.
15x+10y > 1200 x>10
300
6x-5<7x+4
x>-9
300
Solve for c x=4c-b
(x+b)/4=c
300
Mary has 17 different dollar bills. Some are tens and some are ones. She has a total of $62. How many of each does she have?
5 tens and 12 ones
300
find the solution set graphically: y=x+1 3y=-3x+21
(3,4)
300
You are buying cans of soup and boxes of rice. Soup is $2 a can and rice is $1 a box. You have a budget of $16 and you need to buy at least 12 food items in total. Write a system of inequalities.
2x+y<(or equal to) 16 x+y >(or equal to) 12
400
(x^2)+3(x-1)>(x^2)+5
x>8/3
400
Solve for x: (x/5)-7=2w
x=10x-35
400
You purchase 8 gal of paint and 3 brushes for $152.50.The next day, you purchase 6 gal of paint and 2 brushes for  $113.00. How much does each gallon of paint and each  brush cost?
$17 per gallon of paint and $5.50 per brush
400
Multiply: (x-3)(x+4)
(x^2)+x-12
400
You need plates and cups. Plates are $3 and cups are $2. You need 2 times as many cups as plates. You only have $50 to spend. Write an inequality.
3x+2(2x)< (or equal to) 50
500
-5<-2x-7<9
-8<x<1
500
Solve for x rx+h=sx-k
x=(h+k)/(s-r)
500
A clothing maker hass 100 yards of fabric to make shirts and pajamas. A shirt requires 1 yard and pajamas require 2 yards. It takes 2 hours to make a shirt and 3 hours to make pajamas, and there are 1600 hours available to make clothing. Sketch and EXPLAIN your solution set.
x+2y<(or equal to) 1000 2x+3y<(or equal to)1600
500
Jack is 27 years older than Susan. In 5 years time, he will 4 times as old as her. How old is Jack?
Jack is 31 and Susan is 4