Solve for X
Solve for x: 3x + 5 = 20
x=5
How many solutions does the equation x + 5 = x + 5 have?
This letter or symbol is used to represent an unknown number.
What is the inverse operation of addition?
Subtraction
Write an equation for: Five more than twice a number is 11.
2x + 5 = 11
Solve for x:2(x - 4) = 10
x = 9
How many solutions does the equation x + 5 = x + 2 have?
None
This is the number that is multiplied by a variable, such as the 4 in 4x.
Coefficient
To solve x/5 = 10, which operation must you use to isolate x?
Write an equation for: The quotient of a number and 3 is 12.
x/3 = 12
Solve for x: x/4 - 7 =-2
x = 20
If you simplify an equation and end up with 0 = 0, what does that mean?
Infinite answers
This term describes a value that does not change, typically a plain number in an expression.
Constant
When solving a multi-step equation, what term do you usually take care of first?
The constant
A taxi charges 5 dollars plus 2 dollars per mile. If the total bill was 21 dollars, write the equation to find the miles (m)
2m + 5 = 21
Solve for x: 5/3x - 12 = 2x + 9
x = -63
If an equation has the same variable term on both sides but different constants, how many answers are there?
No solutions
This property allows you to multiply a sum when multiplying each addend separately, like a(b + c) = ab + ac
Distributive property
To "undo" a fraction coefficient like 2/3x = 8, what do you need to do?
Translate and solve: Triple a number decreased by 4 is 20.
3x - 4 = 20; x = 8
4(2x + 1.35) = 6/8x + 195/105
x = -0.5
How many solutions does 2(x+3) = 1/3(6x + 21) have?
None
These are terms that have the exact same variable raised to the exact same power.
Like terms
In the equation 2/3(9x + 5) = 8/9x - 3x, what are three possible starting options?
You have 50 dollars and spend 2 dollars a day. Your friend has 20 dollars and saves 3 dollars per day. After how many days will you have the same amount of money?
50 - 2d = 20 + 3d; d = 6 days