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.
Solve if x= 6
3(2x + 4)
48
Calculate:
2x2+ x – 1 = 0
Solutions:
X1=1/2
X2= -1
x2 – 49 = 0
X1= 7
X2 = -7
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.
Solve if x=10
4(5x - 1)
196
x2 – 4x + 4 = 0
X1= X2= 2
x2+ 25 = 0
No solution.
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.
Solve if x=12
4(2x-6)
72
– x2 + 4x – 7 = 0
No solution.
x2 + 8x = 0
X1=0
X2= -8
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
Order and calculate:
3x2 + 1 = – 4x
X1= -1/3
X2=-1
Order and calculate:
x2 = 3x
X=0
X= 3
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
Order and calculate:
3x2 = 5x + 2
X1=2
X2 = - 1/3
Order and calculate:
x2 = – 6x
X=0
X= -6