Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

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. Understanding how to manipulate these equations is essential for finding the value of x that satisfies the equation.

Common Denominator

When dealing with fractions in linear equations, finding a common denominator is crucial for simplifying the equation. The common denominator allows you to eliminate the fractions by multiplying each term by this value, making it easier to solve for the variable. This step is particularly important when the equation contains multiple fractions.

Isolating the Variable

Isolating the variable involves rearranging the equation to get the variable (in this case, x) on one side and all other terms on the opposite side. This process often includes combining like terms and performing inverse operations. Successfully isolating the variable is the final step in solving the equation and finding its solution.