Properties
This property is the property that allows us to switch terms in the expression below:
3x2 + 10 - 8x = 3x2 - 8x + 10
What is the Commutative Property of Addition?
Name the type of expression below
x2 + 3x + 4
What is a trinomial?
If a variable is a solution to an equation, it means that when you plug the variable into the equation, this will happen
What is both sides will be (end up) equal?
An unknown quantity usually represented by letters such as x, y, a, b, c,....
What is a variable?
Take a number x.
Write the expression for the difference of five more than twice the number and six.
What is (2x+5) - 6 ?
or
What is 2x - 1?
This Property allows us to group the multiplied constants, allowing the expression to be simplified later, as shown below
(2a)(4)= (2*4)*a = 8a
What is the Associative Property of Multiplication?
All of these expressions are similar except for one, Name the odd one out
2(x - 4) 2x2y
4x + 3 x3 - 8
What is 2x2y?
Is x= 10 a solution to the equation below:
x2 - 40 = 6x
What is Yes?
Or
What is yes, x= 10 is a solution to this equation?
A known or measurable quantity, such as 1, -5, 0.3, 1/2, and π
What is a constant?
Fill in the blanks
1,3,5,7,9,...
-2,0,2,4,6,...
For consecutive even or odd numbers fill in the pattern if n is the first even or odd number in a series
n, n+2, ___, ___, ___
What is n+4, n+6, n+8?
The Property used twice to solve this equation
3x + 5 = 2x - 4
-2x -2x
x + 5 = - 4
- 5 - 5
x = - 9
What is the Subtraction Property of Equality?
Simplify the expression below
6 (y - x) - 3 (2y - 2x)
What is 0?
When simplifying the equation and solving for x in the equation below, list the first three steps.
-0.5x + 9.75 = -2.25 x + 4.5
What is add 0.5x, subtract 4.5, and divide by -1.75?
or
What is add 2.25x, subtract 9.75 and divide by 1.75?
The constant multiplied by the variable in an expression or equation, found to the left of the variable.
What is the coefficient?
Simplify the expression below:
((x2 + 10y3 + x)(y2 + 4))0
What is 1?
This property is used below to simplify the expression
-2(x+4) = -2x - 8
What is the Distributive property of multiplication over addition?
Write the expression below as a binomial multiplication.
(x + 4)(2x - 6) - (3x - 7)(x + 4)
What is (x + 4)(1 - x)?
Or,
What is (x + 4)(-x + 1)
Solve the equation:
3x + 3 = 3(x + 10)
What is NO SOLUTION?
3x + 3 = 3(x + 10)
3x + 3 = 3x + 30
-3x -3x
3 = 30
False, so no solution
A combination of variables and constants with operations such as multiplication, division, addition and subtraction
What is an expression?
If the radius of a circle is (x+2) find the "perimeter" of the circle, or the circumference.
What is 2π(x + 2)?
Using the properties, the expression below can be simplified to this answer
- 6x(x + 4) + 3(x - 8)
Hint: (x)(x) = x2
What is - 6x2 - 21x - 24?
Take a number n. Write the expression for the product of the difference of the number increased by 10 and twice the number and the sum of seven times the number and two less than four times the number. Simplify.
((n + 10) - 2n)( 7n + (4n - 2))
= (10 - n) (11n - 2)
Acceptable answer: What is (10 - n)(11n - 2)?
= 110n - 20 - 11n2 + 2n
= -11n2 + 112n - 20
What is -11n2 + 112n - 20?
Omar has $80 in ones, fives and ten dollar bills. If five less than twice the one dollar bills he has are tens, and ten less than three times the one dollar bills he has are fives, set up an equation to find out how many one dollar bills he has. Set up the equation with x as one dollar bills.
What is x + 5(3x - 10) + 10(2x - 5) = 80?
A combination of variables and constants ONLY with multiplication and division (terms) that have these same two things can be combined by addition and subtraction
What is the same variable with the same exponent?
A rectangle has a length three more than four times its width. Write (and simplify) a formula to find the length and the width of the rectangle if the perimeter of the rectangle is 56 ft.
What is 10w + 6 = 56?