One-Step Linear Equations
x + 2 = 8
x = 6
2x + 2 = 10
x = 4
x + 3 = 15
+3 +3
x = 18
Adding 3 does not undo positive 3.
What does PEMDAS stand for?
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
What number plus two equals 10?
Eight
x - 2 = -10
x = -8
-3x - 5 = 7
x = -4
-2x = -10
/2 /2
x = -5
Forgot the negative sign on 2
In algebra, operations need to be applied to both sides of the equation. Why?
To keep the equation "balanced" or "equal"
If you are $10.79 in debt and then spend another $31.85 on a credit card, what is your account balance?
-$42
-2x = 30
x = -15
15x + 15 = -15
x = -2
6 - x = -9
-6 -6
x = -15
Forgot the negative on the x
Why are multiplication and division opposites?
They "cancel" to one.
Your base salary is $40,000 plus $5,000 per project completed. How many projects would you need to make $100,000 per year?
12 projects
3 - x = -8
x = 11
3x + 2 = 18
/3 /3
x + 2 = 6
-2 -2
x = 4
Did not follow reverse PEMDAS
or
did not divide all values by 3
Why are addition and subtraction opposites?
They "cancel" to zero
12 pennies + 12 nickels
-x/5 = 55
x = -275
-x/7 + 2 = -3
x = 35
4(x - 2) + 4 = 10
4x - 2 + 4 = 10
4x + 2 = 10
4x = 12
x = 3
Improper distribution AND did not subtract both sides by 2
When solving equations, why do we do "reverse" PEMDAS?
Multiplication and division scale to all terms; doing addition and subtraction are more efficient because we can only "combine like terms"
An investment of $10,000 is gaining simple interest at 6%. How long does the investment need to sit in the account to get $3,000 in interest?
5 years