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

Question

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

Accepted Answer

Hello today we're gonna go ahead and find a value of A. That gives us the solution set three. So what this means the solution set of three. Is that the only solution to the system is X. Is equal to three. So in order to figure out the value of A. That gives us X. Is equal to three. We're gonna go ahead and plug in. X. Is equal to 32 are given equation. So are given equation is nine X minus six divided by a plus six equal to three X. And we're gonna go ahead and replace every X. In this equation with three. Doing so is going to give us nine times three minus six over a plus six is equal to three times three. Now nine times three is going to give us 27 27 minus six is going to give us 21. So we have 21 over a plus six is equal to three times three which is nine. Now in order to sulfur A. We need to go ahead and get a by itself in order to do that. We can subtract six from both sides of this equation and that leaves us with 21 over a equal to three. Now I need to get a out of this denominator in order to do that. We can multiply both sides of this equation by A. Because multiplying both sides of the equation by a while. On the left hand side eight times 21 over A. Is just going to cancel out the A. And the denominator leaving you with 21 3 times A. Is going to give you three. A. So doing so is gonna leave us with 21 equal to three a. And in order to suffer A. I'm just gonna go ahead and divide both sides of this equation by three. And that's going to leave me with a. Is equal to seven, which is the value of A. That we are looking for. So a equals 2. 7 is going to give us X. is equal to three. And that means that the solution to this problem is going to be a. So I hope this video helps you in understanding how to find and solve this type of problem. And I'll go ahead and see you all in the next video.

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

Key Concepts

Algebraic Equations

Solution Set

Substitution Method

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