4-1 Write and Evaluate Algebraic Expression
Evaluate given d = 2
3d - 4
2
What are equivalent expressions?
Expressions that are equivalent in value.
When you expand an expression, which property are you using?
ex) 3(4x - 5) = 12x - 15
Distributive Property
a. What is another word for addition?
b. What is another word for subtraction?
Answers may vary
If the expression q - .25q represents 25% of the original price of an item, write a simplified equivalent expression.
0.75q
Write an expression that represents the height of a tree that began at 6 feet and increases by 2 feet per year. Let y represent number of years.
6 + 2y
or
2y + 6
Use the associative property to write an expression equivalent to (w + 9) + 3
w + ( 9 + 3)
Use the GCF to write the factored form of the expression 12x - 16y
4(3x - 4y)
14m - 5 - 8m
An art teacher enlarges the area of a copy of a painting by 49%. Let d represent the area of the original painting. Write two expressions that represent the new area of the painting.
d + 0.49d
1.49d
What expression can be used to determine the total cost of buying g pounds of grapes for 3.99 per lb and c pounds of cheese for 4.25 per lb?
3.99g + 4.25c
or any answer that is equivalent
Use the commutative property to write an expression equivalent to t + 4 + 3 - 2t, MAKING SURE that the like terms are next to each other.
t - 2t + 4 + 3
Expand x(2y - 4)
2xy - 4x
The width of a rectangle is 5x - 2.5 and the length is 2.5x + 8. Find the perimeter.
15x + 11
Give two expressions that are equivalent to the expression 6(s + 1)
s + s + s + s + s + s + 6
2s + 2s + 2s + 2 + 2 + 2
6s + 6
Answers may vary
Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
2.85g + 3.15c
The distance in feet that Kim swims in a race is represented by 4d - 4, where d is the distance of each lap. What is an expression equivalent to 4d - 4. Explain which property you used.
Answers may vary.
Use the distributive property to write an equivalent expression to;
-0.5(4 - 2 + 8x)
Then simplify the expression by combining like terms.
Step 1: -2 + 1 - 4x
Step 2: -1 - 4x
Given the expressions (8x+2) and (-9x+7)
a. Find the sum
b. Find the difference
a. -1x + 9
b. 17x - 5
The total area, in square feet, of a rectangular stage that has been widen by x feet is represented by
1,400 + 70x. Use the Distributive Property to factor the expression. What does each factor in the equivalent expression tell you about the stage?
70(20 + x)
70 is one dimension and (20 + x) is the other dimension
Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. If he bought 8 gallons of gasoline and 6 cans of oil, how much will he have spent in all?
$41.70
Is 4n - 2k + 7 equivalent to 2k - 4n + 7 , explain your reasoning.
No, the value of 4n changed to - 4n, and -2k changed to 2k.
Give two expressions that are equivalent to 18x + 12 using factoring. One must have a NEGATIVE factor.
6(3x + 2) -6(-3x-2)
3(6x + 4) -3(-6x-4)
2(9x + 6) -2(-9x-6)
Nina has x coins. Clayton has 5 fewer coins than six times the number of coins Nina has. Write an expression for the total number of coins Nina and Clayton have altogether. Then simplify the expression.
7x - 5
You go to a store buy a Jacket and a pair of boots. You have a coupon for 15% off the jacket. You also have a coupon for 10% off the entire purchase. You cannot combine the two coupons. Let j represent the original price of the jacket, and b represent the original price of the boots.
a. Write an expression to represent each discount.
b. If the jacket is $50 and the boots are $45, which coupon would save you the most money?
a. 15% off Jacket: .85j + b
10% off entire purchase: .9j + .9b
b. 15% off the jacket cost $87.50 10% off everything cost $85.50 , therefore 10% off the entire purchase would save you more!