● A variable is a letter which represents an unknown number. Any letter can be used as a variable.
● An algebraic expression contains at least one variable. Examples: a, x+5, 3y – 2z
● A verbal expression uses words to translate algebraic expressions. Example: “The sum of a number
and 3” represents “n+3.”
Review of Terms
● An equation is a sentence that states that two mathematical expressions are equal.
Example: 2x-16=18
To solve an equation means to find the value for the variable that satisfied the equation.
Steps to Solving Equations● Simplify each side of the equation, if needed, by
distributing or combining like terms.● Move variables to one side of the equation by
using the opposite operation of addition or subtraction.
● Isolate the variable by applying the opposite operation to each side.
• First, use the opposite operation of addition or subtraction.
• Second, use the opposite operation of multiplication or division.
● Check your answer.
Examples
● “y” is the variable.● Add 6 to each side to
isolate the variable.● Now divide both sides by
3.● The answer is 5.
● Check the answer by substituting it into the original equation.
3 6 9
6 6
3 15
3 3
5
Check: 3(5)-6=9
15-6=9
y
y
y
Equations with No Solution
5( 2) 13 5
5 10 13 5
x x
x x
Some equations have no solution. That means that no value will work in place of the variable. The solution set is the empty set, {}.
5 5x x 10 13
This is a false statement therefore the equation has no solution.
Try this. . .
2 2
3 4x x
Cross multiply to solve.
2( 4) 2( 3)x x Distribute and solve.
2 8 2 6
2 2
x x
x x
8 6 This is a false statement.No Solution. {}