Math Problem Statement
1/2(3/2y+1/3)=-1/2(y-5/2)
Solution
Let's solve the equation step by step:
Given equation:
Step 1: Eliminate the fractions by multiplying both sides by 2.
Step 2: Distribute on both sides.
On the left-hand side, nothing changes: On the right-hand side, distribute the negative sign: So now we have:
Step 3: Eliminate the fractions by multiplying the entire equation by 6 (the least common denominator of 2 and 3).
Multiplying everything by 6: Simplify:
Step 4: Solve for .
Move all terms involving to one side and constant terms to the other: Now, solve for :
Thus, the solution is:
Would you like more details, or do you have any questions?
Related Questions:
- How can we simplify equations with fractions faster?
- What is the method to solve equations that have variables on both sides?
- What are the steps to solve linear equations with fractions?
- How do you find the least common denominator (LCD) in an equation?
- What are some common mistakes to avoid when solving linear equations?
Tip:
When solving equations with fractions, multiplying through by the least common denominator (LCD) can help eliminate the fractions early, making the equation easier to handle.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Fractions
Distributive Property
Formulas
Distributive Property: a(b + c) = ab + ac
Theorems
Distributive Property
Simplifying Fractions
Suitable Grade Level
Grades 8-10