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

검증된 단계별 안내

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.

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.

Simplify the left-hand side further: Combine the constants in the numerator and simplify the equation to isolate the term involving b.

Subtract 13 from both sides of the equation to isolate the fraction term (7(-6) + 4)/b on the left-hand side.

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.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.