Math Problem Statement
Solution
The equation in the image is:
Let's solve this step-by-step:
Step 1: Simplify the equation
Move all the terms involving to one side and constants to the other side.
Step 2: Combine like terms
The left side has -terms and the right side has constants. First, simplify the -terms.
Combine the fractions:
This gives:
Step 3: Interpret the result
Since both sides of the equation simplify to , this indicates that the equation is true for all values of . Therefore, the solution is that any real number is a solution.
Would you like further details or have any questions?
Here are 5 related questions to explore:
- What are the possible types of solutions in linear equations (one solution, no solution, or infinitely many solutions)?
- How do we handle equations involving fractions with different denominators?
- What is the geometric interpretation of equations that are true for all values of ?
- How would the solution change if the equation had terms with or other powers?
- What strategies can be used to simplify equations with fractions?
Tip: When dealing with fractions in equations, it's often useful to clear them by multiplying through by the least common denominator (LCD).
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Fractions
Formulas
Simplification of linear equations
Combining like terms
Theorems
Linear equation theorem
Zero property of equality
Suitable Grade Level
Grades 8-10
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