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
Evaluate 32.
9
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 x and 1x equivalent expressions?
Yes they are equivalent expressions because they give the same result for every value of the variable.
Use the distributive property to simplify:
4(5x - 1)
20x - 4
Evaluate 34
81
What is the constant in the expression 4x+5y+5+x
5 (a constant is a number without a variable)
What is the algebraic expression for the phrase:
a number divided by 8
n/8
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 simplify:
4(2x-6)
8x-24
Evaluate x3 if x=2
8
What is the coefficient in the expression 4+7x+2
7 (coefficient is the number in front of the variable)
What is the algebraic expression for the phrase:
a number minus 8
x-8
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.
Use order of operations to simplify:
7(2+3)-5/5
34
Evaluate 2w2 + w if w=4
36
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 the phrase:
8 less than twice a number
2x-8
Are x3 and (x)(x)(x) equivalent expressions?
They are equivalent expressions because they give the same result for every value of the variable.
Use order of operations to simplify:
8(3)-(5-4)+32
32
Evaluate 43/r if r=8
True or False: This is an example of an algebraic expression: 5m+1
True (an algebraic expression must include a variable)