In Exercises 1–26, solve and check each linear equation. 11x - (6x - 5) = 40

Verified step by step guidance

1. Start by distributing the negative sign through the parentheses: \(11x - 6x + 5 = 40\).
2. Combine like terms on the left side: \((11x - 6x) + 5 = 40\) simplifies to \(5x + 5 = 40\).
3. Subtract 5 from both sides to isolate the term with \(x\): \(5x + 5 - 5 = 40 - 5\) which simplifies to \(5x = 35\).
4. Divide both sides by 5 to solve for \(x\): \(x = \frac{35}{5}\).
5. Check your solution by substituting \(x\) back into the original equation to ensure both sides are equal.

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 states that a(b + c) = ab + ac, allowing us to multiply a single term by two or more terms inside parentheses. This property is essential for simplifying expressions and solving equations, as it helps eliminate parentheses and combine like terms effectively.

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 occurred during the solving process. It is a crucial part of problem-solving in algebra.