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Simplify the Expression
Vocabulary
Properties
Variable on One Side
Variable on both sides
100
3x + 2x + 4 + 5x - 3
10x + 1
100
This is the number we are multiplying the variable by, which is why we divide by it as our last step to solve.
What is the coefficient?
100
a(b + c) = ab + ac
What is the distributive property?
100
x + 14 = 23
x = 9
100
6g + 7 = 7 + 6g
Infinite solutions
200
3b + 15 - 2b + 8 - (1/2)b - 7
(1/2)b
200
These numbers don't change regardless of what gets plugged in for the variable.
What is a constant?
200
a + (b + c) = (a + b) + c
What is the associative property?
200
3t - 15 = 9
t = 8
200
4r + 12 = 6r - 12
r = 12
300
2(x + 4) - 7 + 4(x + 3) - 5x
x + 13
300
When we simplify an expression, we are combining these things to make it smaller/easier.
What are like terms?
300
This is the most expensive property on a Monopoly board
What is Boardwalk?
300
25 = 5(x - 1)
x = 6
300
4(b - 3) = 16 + 4b
No solution
400
4d - 3w + 2d - 5 + 6w + 12 - 3d + 4w
3d + 7w + 7
400
These are the three types of solutions that we can have when solving equations
What are no solution, one solution and infinite solutions?
400
a + b = b + a
What is the commutative property?
400
40 = 3(x + 5) + 19
x = 2
400
3(x - 5) = 2(x + 8)
x = 31
500
-2(x - 5) + 3z + 2y + 4x - 2z - 3y + 2(x + y)
4x + y + z + 10
500
When our equation has + a number, we - it to make that term 0. This method is called...
Inverse operation
500
When we multiply something by 1, or add 0 to something, it is this property?
What is the identity property?
500
16 = -2(x - 4) - 6x
x = -1
500
4w + 3 + 2w = 5w - 7 + 3
w = -7