Solve each linear equation. See Examples 1–3. 7x + 8 = 1

Verified step by step guidance

1. Identify the given linear equation: \$7x + 8 = 1$.
2. Isolate the term containing \(x\) by subtracting 8 from both sides: \$7x + 8 - 8 = 1 - 8\( which simplifies to \)7x = 1 - 8$.
3. Simplify the right side of the equation: \$7x = -7$.
4. Solve for \(x\) by dividing both sides by 7: \(x = \frac{-7}{7}\).
5. Simplify the fraction to find the value of \(x\).

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 represents a straight line when graphed. Solving a linear equation involves finding the value of the variable that makes the equation true.

Isolating the Variable

Isolating the variable means manipulating the equation to get the variable alone on one side. This typically involves performing inverse operations such as addition, subtraction, multiplication, or division to both sides of the equation to maintain equality.

Properties of Equality

Properties of equality state that you can add, subtract, multiply, or divide both sides of an equation by the same nonzero number without changing the equation's solution. These properties are essential for maintaining balance while solving equations.