Equivalent Expressions
Find the sum of (5a + 3b - 6c) + (2a - 4b +13c)
7a - b + 7c
Your parents are redecorating the dining room and want to place two rectangular wall lights that are 30 inches wide along a 10-foot wall so that the distance between the lights and the distances from each light to the nearest edge of the wall are all the same. Write an equation in standard form to find the distance, x.
3x + 30 = 120
Is n = 2 a solution to 4n - 3 = -2n + 9, show your work.
Yes
Picture 1
x = 2º
The difference between an expression and an equation.
An expression does not include an answer and an equation does.
Subtract (2x + 3y - 4) - (5x + 2)
-3x + 3y - 6
The ages of three sisters are consecutive integers. The sum of their ages is 51. Write an equation to find the ages of the sisters.
x + (x + 1) + (x + 2) = 51 or 3x + 3 = 51
The perimeter of a rectangle is 40 inches. If its length is four times its width, find the dimensions.
Width= 4 inches
Length= 16 inches
Picture 2
x = 17º
What is it called when we are trying to get the variable to be alone?
Isolating the variable
Factor the expression 12x + 84y - 36
12(x + 7y - 3)
Sophia pays a $19.99 membership fee for an online music store. If Sophia purchases 𝑛 songs for $0.99 each, write an expression for the total cost.
0.99n + 19.99
Mrs. Canale’s class is selling frozen pizzas to earn money for a field trip. For every pizza sold, the class makes $5.35. They have already earned $182.90 toward their $750 goal. How many more pizzas must they sell to earn $750?
106 pizzas
Picture 3
Operations that undo each other are called...
Inverse operations
Write 7(4n - 5m - 2) in standard form
28n - 35m -14
Write an equation to represent five more than −8 times a number is 29.
-8x +5 = 29
Shane is 18 years older than Frank. In 6 years, the sum of their ages will be 62. Find their present ages.
Frank is 16 and Shane is 34
Picture 4
x = 1º
Two angles where their sides form two pairs of opposite rays in the shape of an x.
Vertical Angles
Distribute to find an equivalent expression: 5 - 2(3x - 17)
-6x + 39
Write an equation to represent when 4 is subtracted from half of a number the result is 5.
1/2x - 4 = 5
Any borrows a book from a public library. She reads a few pages on day one. On day two she reads twice the number of pages she read on day one. On the third day, she reads six pages less than what she reads on the first day. If she reads a book that contains 458 pages in three days, how many pages did she read on the first day.
116 pages
Picture 5
x = 10º
Two angles that share a common vertex (a point where two lines meet) and a common side (a line segment that both angles touch).
Adjacent angles