In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 3(2x-5)-2(4x+1)=-5(x+3)-2

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term inside a set of parentheses. In the context of the given equation, applying the distributive property is essential for simplifying expressions like 3(2x - 5) and -2(4x + 1) by distributing the coefficients across the terms within the parentheses.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. This step is crucial in solving equations, as it helps to consolidate the equation into a simpler form, making it easier to isolate the variable. In the provided equation, after applying the distributive property, combining like terms will help in further simplification.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This process typically includes isolating the variable on one side of the equation through a series of algebraic manipulations, such as adding, subtracting, multiplying, or dividing both sides by the same number. In the context of the given problem, after simplifying the expression, the next step will be to solve for x by isolating it.