Definitions
According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
A (B – C) = AB – AC
The Distributive Property
Simplify
6n + 3n - 5m + 12 + 9m
4m+9n+12
(5x - 4) + (9x + 5)
14x + 1
What expression represents the phrase
the product of 3 and the difference of x and 2?
3(x-2)
6=2(y+2)
Solve for y.
y=1
Terms whose variables (such as x or y) with any exponents (such as the 2 in x2) are the same
Like Terms
Identify the Coefficients and Constants...
-8a - 3ab + 15b + 9 + 6
Coefficients: -8, -3, 15
Constants: 9, 6
(-x + 4.6) +(-2x - 5.32)
-3x - 0.72
What expression represents the phrase
the sum of 5 times x and 6?
5x + 6
9(p−4)=−18
Solve for p.
p=1
A sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Simplify ...
4x - 3x + 2x + 12 - 19
3x - 7
(x - 1-3.5t)+( -2x+4.1t + 7)
-x + 6 + 0.6t
What expression represents the phrase
the product of -5 and x increased by 4?
-5x + 4
2(x-9) = 9 ÷ (-1/3)
Solve for x.
-4.5
This property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.
The commutative property.
Simplify...
2c - 3d - 5c + 4d + 8
-3c + d + 8
(8b+7)+(6x-4)+(5c+8)
8b+6x+5c+11
What expression would represent
3 less than twice x?
2x - 3
Mia tried to solve an equation step by step.
0.1t−3=5
Step 1: 0.1t=2
Step 2: t=20
Identify her mistake and solve for t. SHOW YOUR WORK!
Mia made a mistake in Step 1. Mia subtracted 3 on both sides instead of adding 3 on both sides.
The correct answer is t=80
In algebra, a symbol standing in for an unknown numerical value in an equation or an algebraic expression. It is a quantity that can be changed and is not fixed.
A variable
Simplify...
12m - 19 x - 3m + 19x + 12 - 18
9m - 6
The width of a rectangle is 5x-2.5 feet and the length is 2.5x+8 feet. Find the perimeter of the rectangle.
15x+11
What expression would represent the phrase
3 more than the quotient of x and 5?
x/5 + 3
n+1/3=3/4
n=5/12