Variables
Expressions
Equations
Solution of an Equation
We can check this solution in the original equation:
A variable is a symbol that represents a number.
An expression is a mathematical statement that may use numbers, variables, or both.
Example:
The following are examples of expressions:
2
x
3 + 7
2 × y + 5
2 + 6 × (4 - 2)
z + 3 × (8 - z)
An equation is a statement that two numbers or expressions are equal. Equations are useful for relating variables and numbers.
Example:
The following are examples of equations:
2 = 2
17 = 2 + 15
x = 7
7 = x
t + 3 = 8
3 × n +12 = 100
w + 4 = 12 - w
y - 1 - 2 - 9.3 = 34
3 × (d + 4) - 11 = 321 - 23
When an equation has a variable, the solution to the equation is the number that makes the equation true when we replace the variable with its value.
Example:
Q:This problem illustrates grouping like terms and dealing with subtraction in an equation.
Solve x - 12 + 20 = 37.
Solition:Replacing the -12 with a +(-12), we get
x + (-12) + 20 = 37.
Since addition is associative, the two like terms (the integers) may be combined.
(12) + 20 = 8
The left side of the equation becomes
x + 8 = 37.
Now we may subtract 8 from each side of the equation, (we will actually add a -8 to each side).
x + 8 + (-8) = 37 + (-8)
x + 0 = 29
x = 29
29 - 12 + 20 = 37x + 0 = 29
17 + 20 = 37
37 = 37 so our solution is correct. 
TRY OUT the practice problems.
In the game the addition sign "+" is denoted as * because of technical problems. sorry for the inconvenience.