In Exercises 1–26, solve and check each linear equation. 16 = 3(x - 1) - (x - 7)

Verified step by step guidance

1. Distribute the 3 into the expression (x - 1) to get 3x - 3.
2. Distribute the negative sign into the expression (x - 7) to get -x + 7.
3. Combine like terms: 3x - x to get 2x, and -3 + 7 to get 4.
4. Set up the equation: 16 = 2x + 4.
5. Subtract 4 from both sides to isolate the term with x: 16 - 4 = 2x.

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form ax + b = c, where a, b, and c are constants, and x is the variable. Solving a linear equation involves isolating the variable to find its value, which satisfies the equation.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. This property allows you to multiply a single term by each term within a set of parentheses. In the context of solving equations, applying the distributive property helps simplify expressions and make it easier to isolate the variable.

Checking Solutions

Checking solutions involves substituting the found value of the variable back into the original equation to verify its correctness. This step ensures that the solution satisfies the equation, confirming that no errors were made during the solving process. It is a crucial part of problem-solving in algebra to validate the results.