In Exercises 25-38, solve each equation. x/4 =2 +(x-3)/3

Verified step by step guidance

1. Multiply every term by the least common denominator (LCD) of the fractions to eliminate the fractions. The LCD of 4 and 3 is 12.
2. Multiply each term by 12: $12\cdot \frac{x}{4}=12\cdot 2+12\cdot \frac{x-3}{3}$.
3. Simplify each term: $3x=24+4(x-3)$.
4. Distribute the 4 on the right side: $3x=24+4x-12$.
5. Combine like terms and solve for $x$.

Key Concepts

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This typically requires isolating the variable on one side of the equation through various algebraic operations, such as addition, subtraction, multiplication, and division. Understanding how to manipulate both sides of the equation is crucial for arriving at the correct solution.

Common Denominators

When dealing with equations that include fractions, finding a common denominator is essential for simplifying the equation. A common denominator allows you to combine or compare fractions more easily. In the given equation, identifying the least common multiple of the denominators (4 and 3) will facilitate the elimination of the fractions, making the equation easier to solve.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. This property is useful when simplifying expressions or equations that involve parentheses. In the context of the given equation, applying the distributive property may be necessary to expand terms and combine like terms, ultimately leading to a simpler form that can be solved for the variable.