Two-Step Equations
Solve the equation:
9 = 4a + 13
a = -1
The sum of three consecutive integers is 255. Write an equation and solve to find the three integers.
Equation: 3x + 3 = 255
Integers: 84, 85, 86
Solve:
12k + 15 = 2k + 35
k = 2
Solve:
6(2x - 3) = 18
x = 3
Solve for x: 4y + x = 10
x = 10 - 4y
Solve the equation:
23 = 11 - 4x
x = -3
The sum of five consecutive integers is 200. Write an equation and find the five integers.
Equation: 5x + 10 = 200
Integers: 38, 39, 40, 41, 42
Solve:
6x + 7 = 8x - 13
x = 10
Solve:
2(3n + 2) = -8
n = -2
Solve for g: gh = 9
g = 9/h
Solve the equation:
6 + (n/5) = -4
n = -50
The sum of four consecutive odd integers is 296. Write an equation and find the integers.
Equation: 4x + 12 = 296
Solution: 71, 73, 75, 77
Solve:
18 + 3w = 4 - 4w
w = -2
Solve:
4(x-3) - 2 = 6
x = 5
Solve for c: 2c - 10 = 5a
c = (5a + 10)/2
or
c = (5/2)a + 5
Solve the equation:
(x+3)/2 = 5
x = 7
Write an equation and solve: Angela rented a car for $29.99 a day plus a one-time insurance cost of $5.00. Her bill was $124.96. For how many days did she rent the car?
Equation: 29.99d + 5 = 124.96
Solution: 4 days
Solve:
38 + 7k = 8(k - 4)
k = 70
Solve:
3(2k - 4) - 6 = 18
k = 6
Solve for m: 6m + 5n = 2n - 12
m = (-3n - 12)/6
or
m = (-1/2)n - 2
Solve the equation:
(a - 4)/3 = -7
a = -17
The Spanish club is selling calendars to raise funds for their annual trip. They plan to sell the calendars for $7.50 each, but the initial cost to print and produce the calendars was $450. If their goal is to raise $3500, how many calendars do they need to sell?
Equation: 7.50c - 450 = 3500
Solution: 527 calendars
Solve:
3(a + 22) = 12a + 30
a = 4
3(a - 5) - 5a = 2a + 9
a = -6
Solve for k: 4k + 6 = 2k - 16g
k = -8g - 3