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Solving Equations in Factored Form
Objective: SWBAT solve an equation in factored form.
Quick Check: Write 3 basic steps to solve an equation
Step 1:
Step 2:
Step 3:
Sometimes an equation includes an expression with
parentheses (distributive property). We can solve these
equations in more than one way.
EQUATIONS AND DISTRIBUTIVE PROPERTY WITH
AN INTEGER
METHOD 1
Distributive Property and Inverse Operation
RULES:
STEP 1: Use the distributive property (distribute the
outside number to all inside numbers)
STEP 2: Combine like terms, if it is required.
STEP 3: Identify the variable.
STEP 4: Identify addition/subtraction operation (constant)
on variable side and undo it by its opposite operation.
Step 5: Identify multiplication/division (coefficient) and
unto it by taking its inverse or reciprocal.
Step 6: Check your work
Example: 2(3x+1)=11
METHOD 1
Step 1:
2(3x) + 2(1)=11 Use the distributive property.
6x + 2 =11
Simplify.
Step 3:
6x + 2 =11
Identify the variable
Step 4:
6x + 2 =11
Undo addition/subtraction (the
Constant).
-2 = -2
_________________
6x = 9
Step 5:
6x/6= 9/6
Undo multiplication/division
(the coefficient)
x = 3/2 or 1.5 or 3 ½
Isolate the variable
METHOD 2
Inverse operation of factor
RULES:
STEP 1: Use inverse operation of the factor on both sides
of the equation to get rid of it.
STEP 2: Combine like terms, if it is required.
STEP 3: Identify the variable.
STEP 4: Identify addition/subtraction operation (constant)
on variable side and undo it by its opposite operation.
Step 5: Identify multiplication/division (coefficient) and
unto it by taking its inverse or reciprocal.
Step 6: Check your work
Example: 2(3x+1)=11
Step 1:
2(3x + 1) = 11 Divide both sides by 2
2
2
3x + 1 = 11
Simplify.
Step 3:
6x + 2 =11
Identify the variable
Step 4:
6x + 2 =11
Undo addition/subtraction (the
Constant).
-2 = -2
_________________
6x = 9
Step 5:
6x/6= 9/6
Undo multiplication/division (the
Coefficient)
x = 3/2 or 1.5 or 3 ½
Isolate the variable
If the factor is a fraction
Example 3:
1/6 (z+1)=6
Method1
1/6 (z) + 1/6 (1) =6
Distribute 1/6
1/6 z + 1/6 = 6 or z/6 + 1/6=6
1/6 z + 1/6 =
6
simplify
Undo addition/subtraction(constant)
-1/6 = -1/6
------------------------1/6 z = 6 + (-1/6)
=6/1 + (-1/6)
=6x6/1x6 + (-1/6)
Solve the fractions
LCD is 6
Turn into equivalent Fractions
=36/6 + (-1/6)
Simplify
=36 + (-1) = 35/6
1/6 z = 35/6
6 x 1/6 z = 35/6 x 6 Undo the coefficient
Z = 35
METHOD 2: INVERSE method
1/6 (Z+1) =6
(6)x 1/6 (z+1) =6(6)
multiply both sides by 6
Z+1=36
simplify
-1=-1
undo the constant(add/sub)
____________
Z = 35
Guided Practice:
1) 1.5(p+3)=18
2) ¼ (q+1)=9
isolate the variable.