Vocabulary
What are "like terms"?
Terms that have the same variable Ex. 2x/ 5x
Expand 8(3j - 4)
24j-32
Write an algebraic expression for
" Seven more than a number"
x + 7
Evaluate 12x+5, if x is 1
The value is 17.
Solve x + 5 = 12
x= 7
What are "equivalent expressions"?
Expressions that produce the same result when the same value is substituted for the variable
Ex. 3n +4n +6 = 7n +6
Factor 14r-8
2(7r-4)
Write the algebraic expression for:
j divided into 3 equal groups, plus 2 more
j/3 + 2
Evaluate 4x/3, where x is 9.
The value is 12.
Solve 3x + 4 = 19
x = 5
What does it mean to factor an expression?
To divide all terms in an expression by their greatest common factor
Ex. 12y-8= 4(3y-2)
Expand and simplify 5(p+5 ) + 4(2p -3)
13p + 13
Write the algebraic expression for
“Seven less than three times a number, divided by five.”
(3y-7)/5
Evaluate 1/5(10 +4x), if x is -1
The value is 1.2 or 6/5
*1/5 X 6 = 6/5 or 1.2*
Solve 4n + 3 = 8n-5
n = 2
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3+ 4n-5
8 =4n
What does it mean to "isolate the variable"?
To change an equation to get a variable alone on one side to determine it's value
Are these expressions equivalent?
9(y-2) and 18-9y
No, because, they are opposite operations.
18−9y=−(9y−18)
9(y-2) = 9y -18
The regular price of the latest Minecraft Game is m dollars. It is on sale for 75% of its regular price.
Write the algebraic expression for its sale price.
The sale price of the game could be written as 0.75m
Evaluate (5x + 8y) / 6, if x is -4, and y is 1/4
The value of the expression is -3
Solve y2 = 132 - 122
y = 5 or -5 ( because (-5)2 also can = 25
What does it mean to evaluate an algebraic expression ?
To find a numerical value of an algebraic expression by substituting a known variable, then simplifying.
Killian factored 16m-12.
They got 2(8m -6), Are they correct? Why?
Partially they are correct. 2 is not the Greatest Common Factor. It is 4.
So his answer should have been 4(4m-3)
Emiko's paycheque was $p. They spent 25% of it. They saved $850 of the amount she had left and donated the rest to Eastview Community Centre.
Determine an expression for the amount she donated to Eastview.
Emiko donated 0.75p - 850 of their paycheque to Eastview.
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Paycheque: p
Spent: p- 0.25p = 0.75p (left)
Saved: 0.75p-850
Or 75% of her paycheque minus $850.
Evaluate 6x + 4y / 3z if x is 2, y is -3, and z is -1/3
The value of the expression is 0.
*12 + (-12) /3(-1/3) = 0/-1*
Solve P= 2(525 +y) + 1504
y= 227