SOLVE EQUATIONS WITH VARIABLES ON EACH SIDE
3x + 4 = 2x + 10
x = 6
GREEN'S GYM CHARGES A ONE-TIME FEE OF $50 AND $30 PER SESSION FOR A PERSONAL TRAINER. BREAKOUT GYM CHARGES AN ANNUAL FEE OF $250 AND $10 FOR EACH SESSION WITH A TRAINER.
50 + 30t = 250 + 10t
t = 10
2(x + 3) = 3x - 6
x = 12
HOW MANY SOLUTIONS:
2x + 4 = 2(x + 2)
INFINITELY MANY
-3x + 12 < 18
x > -2
5x - 2 = 3x + 6
x = 4
RYAN'S RENTALS CHARGES $40 FOR ONE DAY PLUS $0.25 PER MILE. ROAD TRIPS CHARGES $25 FOR THE DAY PLUS $0.45 PER MILE.
40 + 0.25m = 25 + 0.45m
m = 75
3(x - 5) + 2 = x + 7
x = 10
HOW MANY SOLUTIONS:
3x + 1 = 3x + 5
NO SOLUTION
2x + 20 < 34
x < 7
4x + 7 = 3x + 12
x = 5
A CONTAINER HAS 130 GALLONS OF WATER AND IS BEING FILLED AT A RATE OF 1/4 GALLON EACH SECOND. ANOTHER CONTAINER HAS 200 GALLONS OF WATER AND IS DRAINING AT A RATE OF 1/3 GALLON EACH SECOND.
130 + 1/4g = 200 - 1/3g
g = 120
-(4x - 8) = 4x - 8
x = 2
HOW MANY SOLUTIONS:
4(x - 1) = 5x + 2
ONE SOLUTION
2.5x - 10 < 20
x < 12
2(x - 3) = 3(x + 1)
x = -9
BLAKE'S SHIPPING COMPANY CHARGES $7 FOR THE FIRST POUND AND $0.20 FOR EACH ADDITIONAL POUND A PACAKGE WEIGHS. STEVE'S SHIPPING COMPANY CHARGES $5 FOR THE FIRST POUND AND $0.30 FOR EACH ADDITIONAL POUND.
7 + 0.20p = 5 + 0.30p
p = 20
5x + 3 - 2x = 16 + 2x
x = 13
HOW MANY SOLUTIONS:
3(4x - 2) = 6(2x + 1)
NO SOLUTION
20 - 4x > 50
x < -7.5
7x + 5 = 3x + 21
x = 4
A RECTANGULAR BATHROOM WITH SIDE LENGTHS 6x AND 12x. THE PERIMETER IS EQUAL TO 48x - 24; WRITE AN EQUATION THAT REPRESENTS THIS AND SOLVE IT FOR x
(PERIMETER OF RECTANGLE = 2L + 2W)
2(6x) + 2(12x) = 48x - 24
x = 2
6(2x - 3) = 3(x + 3)
x = 3
HOW MANY SOLUTIONS:
5(3x + 3) = 5(x + 2) + 5
ONE SOLUTION
Emily is encouraged to read more than 4 hours each week. It will take her 45 minutes to finish the book she is currently reading, then she will divide the remainder of the time equally among the other six days. Write and solve an inequality to find the minimum number of minutes Emily should read each day.
6x + 45 > 240
x > 32.5
a minimum of 33 days