Equations with Variables on One Side
2x + 5 = x - 3
x = -8
Solve and graph
6p - 18 -2p ≤ -2
p ≤ 4
Solve for t:
d = rt
t = d/r
Write a model: Samantha is organizing a picnic. She is renting a picnic table for $20 and buying sandwiches at $3 each for her guests.
What does x represent?
Model: 20 + 3x
x = # of sandwiches
7(4 - t) = -84
t = 16
5(d - 2) = 2d - 1
d = 3
Solve for y
3x = -8 +2y
y = (3/2)x + 4
Bella’s Burgers charges $10 for a burger plus $1.50 for each extra topping, tax included. Carlos’ Burgers charges $8 for a burger and $2.00 per extra topping (tax included). When will the prices be the same for both places?
Write an equation and solve
10 + 1.50x = 8 + 2x
x = 4 (Both places charge the same amount for a burger with 4 toppings)
4(2x+3)−5x=3x+7
No solution
Solve. 3 - 5(a + 4) ≥ -a + 7
a ≤ -6
Solve for y:
2x + 4y = 8
y = 2 - (1/2)x
Tyler has 4 boxes of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
x = 28 apples in each box
(2/5)x + 3 = 7
x = 10
7+3(4x−5)=−2(x+6)
x = -2/7
Solve. -4 (5x - 2) ≥ 4x + 5
x ≤ 1/8
P = 2 (L + W)
L = (1/2)P - W
Dylan has $110. He wants to buy a book for $20 and some CDs for $15 each. How many CDs can Dylan buy?
x ≤ 6
He can buy at most 6 CDs.
5(2x−3)+4x=18
x = 33/14
(2/5)x - (1/3) = (1/15)x + (2/5)
x = 11/5
4/5(15x + 45) ≥ -6x
x ≥ -2
Solve for y:
3x + 4y − 2x + 5y = 20
y = (20/9) - (1/9)x
You are at the farmer’s market buying oranges. You buy two kinds: Navel oranges at $2.00 per pound, and Blood oranges at $2.40 per pound. You spend $41.60 in total. The number of pounds of Navel oranges you buy is 4 more than 3 times the number of pounds of Blood oranges. How many pounds of each type did you buy?
You bought 4 pounds of blood oranges and 16 pounds of navel oranges.