We appreciate your visit to Which of the following equations have exactly one solution Choose all answers that apply A tex 6x 6 6x 103 tex B tex 103x 6. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure! Let's solve each equation to determine which ones have exactly one solution:
(A) [tex]\(-6x - 6 = -6x - 103\)[/tex]
Start by simplifying both sides of the equation. You'll notice that the [tex]\(-6x\)[/tex] terms on both sides cancel each other out:
[tex]\[-6 = -103\][/tex]
This statement is false because [tex]\(-6\)[/tex] does not equal [tex]\(-103\)[/tex]. Therefore, this equation has no solutions.
(B) [tex]\(-103x - 6 = -6x - 103\)[/tex]
First, let's move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\[-103x + 6x = -103 + 6\][/tex]
Combine like terms:
[tex]\[-97x = -97\][/tex]
Next, solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-97\)[/tex]:
[tex]\[x = \frac{-97}{-97}\][/tex]
[tex]\[x = 1\][/tex]
This equation has exactly one solution, [tex]\(x = 1\)[/tex].
(C) [tex]\(103x - 6 = 103x - 103\)[/tex]
Subtract [tex]\(103x\)[/tex] from both sides:
[tex]\[-6 = -103\][/tex]
This statement is also false, similar to equation (A), since [tex]\(-6\)[/tex] does not equal [tex]\(-103\)[/tex]. Hence, this equation has no solutions.
(D) [tex]\(-6x - 6 = 103x - 103\)[/tex]
Move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\[-6x - 103x = -103 + 6\][/tex]
Combine like terms:
[tex]\[-109x = -97\][/tex]
Now, solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-109\)[/tex]:
[tex]\[x = \frac{-97}{-109}\][/tex]
[tex]\[x = \frac{97}{109}\][/tex]
This equation has exactly one solution, [tex]\(x = \frac{97}{109}\)[/tex].
In summary, the equations that have exactly one solution are (B) and (D). Equation (B) has the solution [tex]\(x = 1\)[/tex], and equation (D) has the solution [tex]\(x = \frac{97}{109}\)[/tex].
(A) [tex]\(-6x - 6 = -6x - 103\)[/tex]
Start by simplifying both sides of the equation. You'll notice that the [tex]\(-6x\)[/tex] terms on both sides cancel each other out:
[tex]\[-6 = -103\][/tex]
This statement is false because [tex]\(-6\)[/tex] does not equal [tex]\(-103\)[/tex]. Therefore, this equation has no solutions.
(B) [tex]\(-103x - 6 = -6x - 103\)[/tex]
First, let's move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\[-103x + 6x = -103 + 6\][/tex]
Combine like terms:
[tex]\[-97x = -97\][/tex]
Next, solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-97\)[/tex]:
[tex]\[x = \frac{-97}{-97}\][/tex]
[tex]\[x = 1\][/tex]
This equation has exactly one solution, [tex]\(x = 1\)[/tex].
(C) [tex]\(103x - 6 = 103x - 103\)[/tex]
Subtract [tex]\(103x\)[/tex] from both sides:
[tex]\[-6 = -103\][/tex]
This statement is also false, similar to equation (A), since [tex]\(-6\)[/tex] does not equal [tex]\(-103\)[/tex]. Hence, this equation has no solutions.
(D) [tex]\(-6x - 6 = 103x - 103\)[/tex]
Move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\[-6x - 103x = -103 + 6\][/tex]
Combine like terms:
[tex]\[-109x = -97\][/tex]
Now, solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-109\)[/tex]:
[tex]\[x = \frac{-97}{-109}\][/tex]
[tex]\[x = \frac{97}{109}\][/tex]
This equation has exactly one solution, [tex]\(x = \frac{97}{109}\)[/tex].
In summary, the equations that have exactly one solution are (B) and (D). Equation (B) has the solution [tex]\(x = 1\)[/tex], and equation (D) has the solution [tex]\(x = \frac{97}{109}\)[/tex].
Thanks for taking the time to read Which of the following equations have exactly one solution Choose all answers that apply A tex 6x 6 6x 103 tex B tex 103x 6. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
