Vocabulary
What do we call a letter that represents a number in an equation?
Variable
What should you do first when solving 3x + 5 = 17
Subtract 5
2x + 3 = 7
2x = 4
x = 4
they forgot to divide by 2. x=2
3x + 4 = 10
x = 2
You bought 3 drinks and paid $9. Each drink costs the same. Write and solve the equation.
3x = 9; x = 3
What is the opposite operation of multiplication?
Division
In (x/2) - 4 = 6, what is the second step?
Multiply by 2
4x - 1 = 7
4x = 8
x = 2
no mistake, it's correct
(x/2) - 1 = 5
x = 12
A gym charges $25/month plus a $50 joining fee. You pay $125 total. Write an equation and solve.
25x + 50 = 125; x = 3 months
What is the word for keeping both sides of the equation equal?
Balance
List the two steps needed to solve 5x - 2 = 13
Add 2, then divide by 5
(x/5) + 2 = 6
(x/5) = 4
x=1
You have to multiple 4 by 5, x = 20.
-4x + 8 = 0
x = 2
You earn $12/hour plus $30 in tips. You earned $102 total. How many hours? Write an equation and solve.
12x + 30 = 102; x = 6
What do we call the number added or subtracted to the variable term?
Constant
What's wrong with solving 2x + 3 = 11 by dividing first?
It breaks the order of solving two-step equations. Subtract first.
-3x = 6
x = -2
(x/3) + 5 = 11
x = 18
(x/4) = 18; x = 72
What does it mean to "isolate the variable"?
Get the variable alone on one side of the equation
Describe how you would solve (x/3) + 6 = 10 using inverse operations.
Subtract 6, then multiply by 3
(x/2) - 4 = 6
(x/2) = 10
x = 5
should multiply by 2, x = 20
2x - 3 = x + 5
x = 8
A teacher spends $3 per student supplies, plus $24 on storage. She spent $75 total. How many students? Write an equation and solve it.
3x + 24 = 75; x =17