Solving Multi- Step Equations
1 − 3x = 3x + 1
x=0
y=1/3x - 3
y= -x + 1
(3,-2)
Jason and Maggie collect baseball cards. Jason has 1 and each month gets 2 new ones. Maggie has 3 and each month she gets 1 new one. When will they have the same number of baseball cards?
2 months
3x + 1 = 3(x - 1) + 4
infinite solutions
3v + 2 = 4v + 4
v= -2
y= 3x - 4
y= -1/2x + 3
(2,2)
In Lily’s garden, there are 5 rose bushes the first year. Each year, she adds two new rose bushes. She has 20 tulip plants the first year and loses 3 each year. When will the number of rose bushes equal the number of tulip plants?
3 years
4(x + 1) = 4(2 - x)
x=1/2
4n − 1 = 6n + 8 − 8n + 15
n=4
y = -1
y= -5/2x + 4
(2,-1)
Joe and Steve are saving money. Joe starts with $105 and saves $5 per week. Steve starts with $5 and saves $25 per week. After how many weeks do they have the same amount of money?
5 weeks
2x - x + 7 = x + 3 + 4
infinite solutions
−6 p + 7(1 + 3p) = 2(7 + 8p)
p=-7
y= -2x + 2
y= -2x - 2
no solution
On February 10th there was 4 inches of snow on the ground in Vermont and snowing at a rate of .5 inches per day. In New Hampshire on the same day there was 6.5 inches of snow on the ground and snowing at a rate of .25 inches per day. When will they have the same amount of snow on the ground?
10 days
12 + 2x - x = 9x + 6
x=3/4
2(1 + 6x) + 2(3 − 6x) = 7x − 5x
x=4
y= -1/2x - 2
y= -3/2x + 2
(4,-4)
Two pools are filling up at a constant rate. Ben’s pool had 5 feet of water in it already and fills at a rate of 3 feet per hour. Anna’s pool had 11 feet of water in it already and fills at a rate of 2 feet per hour. When will they have the same amount of water in the pool?
6 hours
3 + 2/3x + 4 = 4x-5/2x
no solution