In Exercises 1–26, solve and check each linear equation. 2x - 7 = 6 + x

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 on one side of the equation to find its value.

Isolating the Variable

Isolating the variable is a fundamental technique in solving equations, where the goal is to manipulate the equation so that the variable appears alone on one side. This often involves performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the equation to maintain equality.

Checking Solutions

Checking solutions is the process of substituting the found value of the variable back into the original equation to verify that both sides are equal. This step is crucial to ensure that the solution is correct and satisfies the equation, confirming that no errors were made during the solving process.