Solve and check each linear equation. 2x - 7 = 6 + x

Verified step by step guidance

1. Start with the given linear equation: \$2x - 7 = 6 + x$.
2. Isolate the variable terms on one side by subtracting \(x\) from both sides: \$2x - x - 7 = 6 + x - x\(, which simplifies to \)x - 7 = 6$.
3. Next, isolate the variable term by adding 7 to both sides: \(x - 7 + 7 = 6 + 7\), which simplifies to \(x = 13\).
4. The solution to the equation is \(x = 13\).
5. Check the solution by substituting \(x = 13\) back into the original equation: verify that \$2(13) - 7\( equals \)6 + 13$.

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.

Isolating the Variable

Isolating the variable means rearranging the equation to get the variable alone on one side. This involves using inverse operations such as addition, subtraction, multiplication, or division to simplify the equation step-by-step until the variable's value is found.

Checking the Solution

After solving the equation, substituting the solution back into the original equation verifies its correctness. This step ensures that the value satisfies the equation and helps identify any errors made during the solving process.