Solving Equations

Creating Equations

100

Three consecutive numbers have a sum of 75. What is the smallest number?

The smallest number is 24.

200

If Austin scores a 78 and 85 on his first two tests, what does he need to score on his third test to average an 87 for all three?

Austin needs to score a 98.

300

If the side lengths of a triangle are three consecutive odd numbers, and the perimeter is 51 cm, what is the length of the longest side?

The longest side is 19 cm.

400

If three consecutive even numbers have a sum of 84, what is the largest number?

What is 30?

500

I am thinking of a number, when I take the square root of this number, and add 1, I get the square root of 100. 

What is 81

Definitions

100

a mathematical statement which shows that two expressions are equal

Equation

200

Distributive Property

What is the property that lets you distribute the multiplication over addition/subtraction inside parentheses

300

isolate the variable 

What is the process of using opposite operations to move numbers and terms so that the variable is alone on one side of the equation 

400

Mean or Average

what is the central value you get when you add up all the numbers and then divide by how many numbers there are.

500

Like Terms 

Hint: They have two things in common

What is the Same variable and the Same Power terms that are "like" each other 

Order of Operations

100

What is the first step?

−6n= 16+2n

Combine like Terms

200

What property should I use to combine like terms?

4(y-2)=7

Distributive Property

300

If the y-intercept of a line is -4 and the slope is 6, what is the equation of the line in slope intercept form.

y = 6x - 4

400

15 + b = 23

b=8

500

−15 + n = −9

n=6

Solving Equations

100

Solve x:

2x + 6 =0

x = -3

200

Solve: 2x - 18 = -3x + 27

x = 9

300

Solve: 7x + 42 = -3x - 28

x = -7

400

Solve: 22 = 2(4h−9)

x =5

500

Solve: 5(3x+10) = 215

What is x =11

Operation/ Inverse

100

-4x + 7 = 11

Operation: x is mult. by -4, 7 is added

Inverse: add -7 to both sides, divide by -4

200

-4 = 2p + 10

Operation: p is multiplied by 2, 10 is added

Inverse: subtract 10, divide by 2

300

2(d + 6) = -10

Operation: add 6 to d, multiply d+6 by 2

Inverse: divide d+6 by 2, divide -10 by 2

400

6(x+3)+13= 85

Operation: add 13, add 3 to x, multiply x+3 by 6

Inverse: subtract 13, divide by 6, subtract 3

500

14 = 3(x – 2) + 5

Operation: add 5, multiply by 3, subtract 2

Inverse: subtract 5, divide by 3, add 2