Math Problem Statement
Solution
The equation in the image is as follows:
Let’s solve step-by-step:
Step 1: Expand both sides
Expand the terms inside the parentheses:
Left-hand side: So the left-hand side becomes:
Right-hand side: Simplify: Add 1 to this:
Step 2: Write the equation
The equation now is:
Step 3: Eliminate fractions
The least common denominator (LCD) of 5 and 2 is 10. Multiply the entire equation by 10 to eliminate the fractions:
Simplify both sides:
Step 4: Combine like terms
Bring all terms involving to one side and constants to the other:
Step 5: Solve for
Divide both sides by 27:
Final Answer:
Would you like a detailed explanation of any step?
5 Related Questions:
- How do you solve equations with fractions efficiently?
- What strategies are useful when expanding and simplifying terms in algebra?
- How can you determine the least common denominator of multiple fractions?
- Why is isolating the variable important in solving linear equations?
- How can you check if the solution is correct?
Tip:
When solving equations with fractions, always consider clearing the fractions by multiplying through by the least common denominator (LCD) to simplify calculations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Fractions
Formulas
Distributive property: a(b + c) = ab + ac
Clearing fractions using the least common denominator (LCD)
Theorems
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Suitable Grade Level
Grades 8-10