6-1: Understand Equations & Solutions
c - 8 = 25
is c = 33 a solution of the equation?
33 - 8 = 25 ✅
c = 33 is a solution
When you are applying a Property of Equality (Addition, Subtraction, Multiplication, or Division) to an equation, you do the ____ operation on both sides of the equation.
When you are applying a Property of Equality (Addition, Subtraction, Multiplication, or Division) to an equation, you do the SAME operation on both sides of the equation.
What is the inverse operation of addition?
subtraction
addition and subtraction are INVERSE OPERATIONS, or oppossites
What is the inverse operation of division?
multiplication
multiplication and division are INVERSE OPERATIONS, or opposites
f - 13 = 28
is f = 38 a solution of the equation?
38 - 13 = 28 ❌
f = 38 is NOT a solution
If 6 + 2 = 8,
Is 6 + 2 + 3 = 8 + 3?
Why or why not?
Yes, because 3 was added to both sides
x + 2 = -11
You can ISOLATE (GET BY ITSELF) the variable by using the ___________ Property of Equality and ___________ 2 from both sides of the equation.
x + 2 = -11
You can ISOLATE (GET BY ITSELF) the variable by using the SUBTRACTION Property of Equality and SUBTRACTING 2 from both sides of the equation.
2a = -22
You can ISOLATE (GET BY ITSELF) the variable by using the ___________ Property of Equality and ___________ 2 from both sides of the equation.
2a = -22
You can ISOLATE (GET BY ITSELF) the variable by using the DIVISION Property of Equality and DIVIDING BY 2 on both sides of the equation.
2y = 30
y = 10, 12, 15, 18
Which value of the variable, if any, is a solution of the equation?
2 * 10 = 30 ❌
2 * 12 = 30 ❌
2 * 15 = 30 ✅
2 * 18 = 30 ❌
y = 15 is a solution
6x = 24
6x * 4 = 24 * 4
What Property of Equality is displayed?
The Multiplication Property of Equality.
4 is multiplied on both sides of the equation.
c + 2 = -11
Solve for c
c + 2 = -11
c + 2 - 2 = -11 - 2
c = -13
2y = -22
Solve for y
2y = -22
2y ➗ 2 = -22 ➗ 2
y = -11
f - 13 = 28
f = 38, 42, 45, 51
Which value of the variable, if any, is a solution of the equation?
38 - 13 = 28 ❌
42 - 13 = 28 ❌
45 - 13 = 28 ❌
51 - 13 = 28 ❌
No solution is given
If 10a + 6 = 26,
Is (10a + 6) ➗ 2 = 26 ➗ 13?
No
Both sides are not divided by the same number
x - 236 = 450
Solve for x
x - 236 = 450
x - 236 + 236 = 450 + 236
x = 686
-7x = 77
Solve for x
-7x = 77
(-7x) ➗ -7 = 77 ➗ -7
x = -11
150 ➗ h + h = 53
h = 2, 3, 4, 5
Which value of the variable, if any, is a solution of the equation?
150 ➗ 2 + 2 = 53 ❌
150 ➗ 3 + 3 = 53 ✅
150 ➗ 4 + 4 = 53 ❌
150 ➗ 5 + 5 = 53 ❌
h = 3 is a solution
When we want to un-do a certain Property of Equality, we can use the Property of Equality with the _______ operation.
When we want to un-do a certain Property of Equality, we can use the Property of Equality with the INVERSE/OPPOSITE operation.
x +21.9 = 27.1
Solve for x
x + 21.9 = 27.1
x + 21.9 - 21.9 = 27.1 - 21.9
x = 5.2
x ➗ 20 = 120
Solve for x
x ➗ 20 = 120
(x ➗ 20) 20 = (120) 20
x = 2,400