One-Step Equations
y + 0.4 = 2.6
y=2.2
3v − 12 = 15
v = 9
What is a variable?
A symbol or letter that represents an unknown variable
Combine the like terms.
5x2 + 3x - x + 2 - 4x2
x2 + 2x + 2
r=-7.8
w/4 -9 =-3
w = 24
What is a coefficient?
The number being multiplied to a variable
Factor the expression.
4x + 32
4(x + 8)
t/-11=11
t=-121
Kimmy earns a $200 commission on every sale plus a base salary of $30,000. Her total income last year was $80,000. Write an equation that can be used to calculate the number of Kimmy’s sales.
30,000 + 200x = 80,000
What is a constant?
A number that is being added or subtracted to a variable
Simplify the expression.
(-4x + 2) - (x + 6)
-5x - 4
2/5n=4
n=10
Juma earns $12.50 for each newspaper subscription he sells. He also earns a $50 base salary each week. If he wants to earn $400 next week, how many newspaper subscriptions does he need to sell?
Write an equation and solve.
50 + 12.50x = 400
x = 28
What are inverse operations?
Opposites
Addition and subtraction
Multiplication and division
Simplify the expression.
14 - 6(3x - 7)
-18x + 56
Write and solve an equation.
A swimmer swam 48 kilometers in x days. What is the value of x if the swimmer swam an average of 3.2 kilometers daily?
3.2x = 48
x = 15
Paco solved the equation −3x − 5 = 1. His work is shown below.
Step 1: −3x − 5 = 1
Step 2: −3x = 6
Step 3: x = 2
Where did Paco make an error in his calculation? Explain.
When he divided 6 by -3, he got 2, but 6 ÷ -3 = -2.
What is the difference between an expression and an equation?
An equation has an equal sign while an expression does not
A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game booth is $50 plus $7 per day.
Write an expression for how much both booths will cost for the same number of days.
100 + 5d + 50 + 7d
150 + 12d