Math Problem Statement
Solution
Let's solve the given equation step by step.
The equation is:
Step 1: Distribute the fractions.
Expand the terms that have fractions:
Now the equation becomes:
Step 2: Simplify constants.
First, handle the subtraction of 2 on the left-hand side:
Now the equation is:
Step 3: Combine constants on the right-hand side.
Simplify the constants on the right-hand side:
Now the equation is:
Step 4: Eliminate the fractions by multiplying through by 3.
To simplify further, multiply both sides of the equation by 3 to eliminate the fractions:
This gives:
Step 5: Solve for .
Now subtract from both sides:
Simplify:
Add 2 to both sides:
Thus, the value of is .
Final Answer:
Would you like more details on any step? Here are some related questions you might want to explore:
- How do you solve equations involving fractions?
- How does distributing work with fractional coefficients?
- What techniques can simplify solving multi-step equations?
- Can you explain the logic behind multiplying both sides by the same value?
- How do you check if a solution to an equation is correct?
Tip: When working with equations that involve fractions, a good strategy is to eliminate fractions early by multiplying the entire equation by the least common denominator (LCD).
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Math Problem Analysis
Mathematical Concepts
Algebra
Solving Linear Equations
Fractions
Formulas
Distributive Property
Combining Like Terms
Solving for x
Theorems
Basic algebraic principles
Multiplication property of equality
Suitable Grade Level
Grades 8-10
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