Exercises 137–139 will help you prepare for the material covered in the next section. Solve for x: a(x - 2) = b(2x + 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 = cx + d, where a, b, c, and d are constants. Solving these equations involves isolating the variable, often by performing operations such as addition, subtraction, multiplication, or division on both sides of the equation.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside parentheses. In the context of the given equation, applying the distributive property is essential for expanding both sides before isolating the variable x.

Isolating the Variable

Isolating the variable is a key step in solving equations, where the goal is to get the variable (in this case, x) alone on one side of the equation. This often involves rearranging the equation and performing inverse operations to eliminate other terms. Mastering this technique is crucial for finding the value of x in linear equations.