Pre-Algebra Examples

Write in Standard Form 7/2x+7/3y=91/3
Step 1
The standard form of a linear equation is .
Step 2
Find the LCD of and .
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Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
Step 2.3
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 2.4
Since has no factors besides and .
is a prime number
Step 2.5
Since has no factors besides and .
is a prime number
Step 2.6
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.7
Multiply by .
Step 3
Multiply both sides by .
Step 4
Simplify the left side.
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Step 4.1
Simplify .
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Step 4.1.1
Simplify each term.
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Step 4.1.1.1
Combine and .
Step 4.1.1.2
Combine and .
Step 4.1.2
Simplify terms.
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Step 4.1.2.1
Apply the distributive property.
Step 4.1.2.2
Cancel the common factor of .
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Step 4.1.2.2.1
Factor out of .
Step 4.1.2.2.2
Cancel the common factor.
Step 4.1.2.2.3
Rewrite the expression.
Step 4.1.2.3
Multiply by .
Step 4.1.2.4
Cancel the common factor of .
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Step 4.1.2.4.1
Factor out of .
Step 4.1.2.4.2
Cancel the common factor.
Step 4.1.2.4.3
Rewrite the expression.
Step 4.1.2.5
Multiply by .
Step 5
Simplify the right side.
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Step 5.1
Simplify .
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Step 5.1.1
Cancel the common factor of .
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Step 5.1.1.1
Factor out of .
Step 5.1.1.2
Cancel the common factor.
Step 5.1.1.3
Rewrite the expression.
Step 5.1.2
Multiply by .
Step 6