Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.

Verified step by step guidance

1. Start by substituting the given solution x = -6 into the equation (7x + 4)/b + 13 = x. This substitution will allow us to solve for the unknown b.
2. Replace x with -6 in the equation: (7(-6) + 4)/b + 13 = -6. Simplify the numerator of the fraction by performing the multiplication and addition.
3. Simplify the left-hand side further: Combine the constants in the numerator and simplify the equation to isolate the term involving b.
4. Subtract 13 from both sides of the equation to isolate the fraction term (7(-6) + 4)/b on the left-hand side.
5. Solve for b by multiplying both sides of the equation by b and then isolating b. This will give you the value of b that satisfies the equation.

Key Concepts

Algebraic Equations

An algebraic equation is a mathematical statement that asserts the equality of two expressions. In this context, we are solving for the variable 'b' in the equation (7x + 4)/b + 13 = x, which requires manipulating the equation to isolate 'b' while ensuring that the solution set includes the specific value of x, which is -6.

Substitution

Substitution is a method used in algebra to replace a variable with a specific value to simplify an equation. In this problem, we will substitute x with -6 to determine the value of 'b' that satisfies the equation, allowing us to find the necessary conditions for the equation to hold true.

Solution Set

A solution set is the collection of all values that satisfy a given equation. In this case, the solution set is specified as {-6}, meaning we need to find the value of 'b' such that when x equals -6, the equation holds true. Understanding the concept of a solution set is crucial for determining the correct parameters of the equation.