Solving Equations
3x + 2 = 8
x = 2
Lucas buys a high-end mountain bike costing $1,200. He makes an initial down payment of $300 and agrees to settle the rest in 6 equal monthly payments, x. Write an equation that models the scenario.
6x + 300 = 1200
5x + 10
What is the inverse of addition?
3(-4b + 5) = 39
b = -2
A fitness center offers a membership valued at $540. To join, members pay a one-time registration fee of $60 and a monthly rate, r, for 12 months. Write an equation that represents this payment structure.
12r + 60 = 540
10(x + 3) - 3
10x - 27
What is the inverse of subtraction?
Addition
x + 2 = x - 5
DNE or No Solution
An auto-repair shop charges Harper $680 to fix her vehicle’s transmission. The cost includes a fixed price of $230 for new parts, plus 5 hours of labor billed at a constant hourly rate, h. Write an equation that models the auto-repair invoice layout.
5h + 230 = 680
7(x + 4) = 49
What is the inverse of multiplication?
Division
8 - 4a= 2a + 11
a = - 1/2
Chloe builds a deck for $2,400. The concrete foundation cost $450 and the rest is distributed evenly among 15 equal bundles of lumber, L. Write an equation mapping the material expenses.
15L + 450 = 2400
10(2x + 4) = 20
x = -1
What is the inverse of division?
Multiplication
40(3x + 25) = 80
x = - 23/3
Jackson purchases a lawnmower for $1,650. He pays a cash down payment of $450 and finances the rest in 8 equal monthly billing payments, p. Write an equation that models this purchasing arrangement.
8p + 450 = 1650
3(x + 7) + 6 = 36
x = 3
What is the inverse of squaring?
Square rooting