Translating Phrases
What is the algebraic expression for the phrase:
a number increased by 8
x+8 (you may choose any variable you want)
Are 3x + 1 and 2x + 2 equivalent expressions? Explain your thinking.
They are not equivalent expressions because they will not always give the same result for every value of the variable. For example if x=0, then 3x+1=3(0)+1=1 and 2x+2=2(0)+2=2. Since 1 and 2 are not the same result they are not equivalent.
Use the distributive property to simplify:
3(2x + 4)
6x + 12
Simplify the following expression: 3 + 8p + 3r - 4p + 6p + 1 - r
10p+2r+4
How many terms does 3x+4+2x+7x
Four terms (3x,4,2x,7x)
What is the algebraic expression for the phrase:
8 decreased by a number
8-x
Are the expressions equivalent?
2(6x - 8) = 2(6x) - 2(8)
Yes
Use the distributive property to simplify:
4(5x - 1)
20x - 4
Jim is j years old. Alex is 4 years younger than Jim. Write an expression to indicate how old is Alex in terms of j?
j-4
What is the constant in the expression 4x+5y+5+x
5 (a constant is a number without a variable)
Write an algebraic expression for;
7 more than 3 times p
3p + 7 or
7 + 3p
Are x + x + x and 3x equivalent expressions?
They are equivalent expressions because they give the same result for every value of the variable.
Use the Distributive Property to expand 1/5(10t-15)
2t - 3
Solve for X
2x=36
x=18
What is the coefficient in the expression 4+7x+2
7 (coefficient is the number in front of the variable)
Write an algebraic expression for;
6 less than the product of 8 and k
8k - 6
Are 4x and 4x equivalent expressions?
They are not equivalent expressions because they will not always give the same result for every value of the variable. If you substitute a value in for x you will get a different result for each expression. For example, if x=2; then 4x=4•2=8 and 4x=42=16.
Expand using Distributive Property:
-2(-4 + 8x)
8 - 16x
Evaluate the following expression if x=3:
(15+x)/(3x-3)
(15 + 3) / (3 x 3 - 3)
18 / 6
3
What are the like terms in the expression 4y+6+9y
4y and 9y (like terms have the same variables--they look exactly the same)
What is the algebraic expression for;
14 less than twice a number
2n-14
Are x3 and (x)(x)(x) equivalent expressions?
They are equivalent expressions because they give the same result for every value of the variable.
Expand AND SIMPLIFY using Distributive Property:
9(4a + 6b - 2) - 2b
36a + 52b - 2
If Mr. Atkins ran 10 miles in 80 minutes and Mr. McGough ran 2 1/4 miles in 18 minutes, who ran faster.
Bonus: Who was more tired at the end?
They both ran at the same rate.
Mr Atkins: Mile time = 80/10 = 8 mins
Mr McGough: Mile time 18/1 / 9/4 = 18/1 * 4/9= 8 mins.
Bonus: Neither was tired, we are used to running around school with our carts!
True or False: This is an example of an algebraic expression: 5m+1
True (an algebraic expression must include a variable)