Math Problem Statement
Solve using the addition and multiplication principles together. Do not forget to check. one third y minus three fourths y plus 7 equals five twelfths plus one fourth y 1 3y− 3 4y+7= 5 12+ 1 4y
Solution
We are given the equation:
Step 1: Eliminate the fractions
To make things simpler, we will eliminate the fractions by multiplying the entire equation by the least common denominator (LCD) of the fractions. The denominators are 3, 4, and 12, and the LCD of these numbers is 12.
Multiply the entire equation by 12:
This gives:
Step 2: Simplify both sides
Simplify the left and right sides:
Step 3: Get all the -terms on one side
To move the -terms to one side, subtract from both sides:
Step 4: Isolate the -term
Subtract 84 from both sides:
Step 5: Solve for
Divide both sides by -8:
Step 6: Check the solution
Substitute back into the original equation:
The left-hand side simplifies to:
The right-hand side simplifies to:
Both sides are equal, so the solution is correct.
Would you like to go over any details or ask questions?
Here are 5 related questions for further exploration:
- How do you find the least common denominator (LCD) for fractions?
- How would you solve the equation if there were decimals instead of fractions?
- What would the solution be if the constants on the right-hand side were negative?
- How do we deal with equations that have no solutions?
- Can you solve this type of equation using substitution?
Tip: Always check your solution by plugging it back into the original equation to verify!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Fractions
Simplification
Formulas
Multiplication Principle for Fractions: Multiply both sides by the least common denominator (LCD) to eliminate fractions.
Theorems
Addition and Multiplication Principles for Solving Equations
Suitable Grade Level
Grades 8-10