Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2

Verified step by step guidance

1. Start by eliminating the fractions. Multiply every term by the least common denominator (LCD) of the fractions, which is 6 in this case.
2. Distribute the 6 to each term: 6(20) - 6(x/3) = 6(x/2).
3. Simplify each term: 120 - 2x = 3x.
4. Rearrange the equation to get all terms involving x on one side: 120 = 3x + 2x.
5. Combine like terms: 120 = 5x, then solve for x by dividing both sides by 5.

Key Concepts

Linear Equations

Linear equations are mathematical statements that express the equality of two linear expressions. They typically take the form ax + b = c, where a, b, and c are constants, and x is the variable. Solving linear equations involves isolating the variable to find its value, which can be done through various methods such as addition, subtraction, multiplication, or division.

Fractions and Denominators

Fractions represent a part of a whole and consist of a numerator and a denominator. In the context of linear equations, constants in the denominators can complicate the solving process. To eliminate fractions, one common technique is to multiply both sides of the equation by the least common denominator (LCD), which simplifies the equation and makes it easier to solve.

Isolating the Variable

Isolating the variable is a fundamental step in solving equations, where the goal is to get the variable (e.g., x) alone on one side of the equation. This often involves performing inverse operations to both sides of the equation, such as adding, subtracting, multiplying, or dividing. Successfully isolating the variable allows for determining its value, which is the solution to the equation.