Variable on Both Sides
2x + 3 = 5x
x + x = 14
x = 7
2(x + 1) = 10
x = 4
7x + 11 = 11 + 7x
Infinite Solutions
What do you call the unknown term that you are trying to solve for?
Variable
7 + x = 2x
x = 7
3x + 5x = 21 + 11
x = 4
3(2x + 10) = 60
x = 5
3(x + 2) = 3x + 7
No Solution
What number can't we divide by?
Zero
5 + x = 3x + 1
x = 2
3x + 3 - x = 5 + 3x - 5
x = 3
(4 + x)2 = 8
x = 0
-(x + 3) = x - 9 + x
x = 2
How do you know if your equation will have infinitely many solutions or no solutions?
Infinitely many -> equation always true
No solutions -> equation always false
19 - 5x = 5x + 9
x = 1
Infinite Solutions
-5(8 + x) = 3x
x = -5
3(x + 5) = (4 + x)2
x = -7
Find the following inverses:
addition ->
multiplication ->
square ->
addition -> subtraction
multiplication -> division
square -> square root
7x + 9 = 15 + 7x
No Solutions
15x - 11 - 7x = 2 + 3x + 2
x = 3
5 - 3(3 + 2x) = 6 + 4x
x = -1
5 - 3(3 + 2x) = 6 + 4x
x = -1
What is the equation for slope-intercept form?
y = mx + b