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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

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After studying this lesson, you will be able to:

• Solve equations containing fractions.

To Solve Equations containing fractions:

Clear out the fractions by multiplying the ENTIRE equation by the common denominator.

SPECIAL CASES

Sometimes when dealing with equations, all the variable cancel out. When this happens we have a "special case". If the expression we're left with is a true mathematical statement, our solution is called the Identity Property which means that there is an infinite number of solutions. The symbol for infinity is . If the expression we're left with is a false mathematical statement, there will be no solution. We indicate this with the empty set symbol which is Ø.

Example 1

 2x + 5 = 2x -3 To solve this equation, we need to attempt to get the variables together on the same side. 2x + 5 - 2x = 2x -3 - 2x When we subtract 2x from each side, all variables are eliminated, leaving us with 5 = -3 5 = -3 We know this is a "special case" since we have no variables. Since 5 is not equal to -3, this is a false statement. Therefore there are no solutions. Ø We write the empty set symbol for our answer

Example 2

 3 ( x + 1 ) - 5 = 3x -2 To solve this equation, we first remove the parentheses by distributing. 3x + 3 - 5 = 3x - 2 We need to collect like terms (3 - 5 ) on the left side 3x - 2 = 3x -2 To solve this equation, we need to attempt to get the variables together on the same side. 3x - 2 - 3x = 3x -2 - 3x We do this by subtracting 3x from each side. This gives us -2 = -2 -2 = -2 We know this is a "special case" since we have no variables. Since -2 is equal to -32, this is a true statement (the identity property). Therefore there are infinite number of solutions. We write the symbol for infinity for our answer