In Exercises 1–26, solve and check each linear equation. 7x + 4 = x + 16

Verified step by step guidance

1. Start by writing down the given equation: \$7x + 4 = x + 16$.
2. To isolate the variable terms on one side, subtract \(x\) from both sides: \$7x - x + 4 = 16$.
3. Simplify the left side by combining like terms: \$6x + 4 = 16$.
4. Next, subtract 4 from both sides to isolate the term with \(x\): \$6x = 16 - 4$.
5. Finally, divide both sides by 6 to solve for \(x\): \(x = \frac{16 - 4}{6}\).

Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It forms a straight line when graphed and typically has the form ax + b = c. Understanding how to manipulate and solve these equations is fundamental in algebra.

Solving Linear Equations

Solving a linear equation involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, and division. The goal is to find the value of the variable that makes the equation true.

Checking Solutions

After finding a solution, substituting it back into the original equation verifies its correctness. This step ensures that no mistakes were made during solving and confirms the solution satisfies the equation.