We appreciate your visit to Which of the following equations have infinitely many solutions Choose all answers that apply A tex 76x 76 76x 76 tex B tex 76x 76. 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 :
To determine which of the given equations have infinitely many solutions, we will examine each equation:
(A) [tex]\(-76x + 76 = 76x + 76\)[/tex]
1. Start by moving all the terms involving [tex]\(x\)[/tex] to one side of the equation:
[tex]\(-76x - 76x = 76 - 76\)[/tex]
2. Combine like terms:
[tex]\(-152x = 0\)[/tex]
3. Divide both sides by [tex]\(-152\)[/tex]:
[tex]\(x = 0\)[/tex]
For equation (A), if you substitute [tex]\(x = 0\)[/tex], it satisfies the equation, indicating that [tex]\(x = 0\)[/tex] is a solution. Since the form suggests [tex]\(0 = 0\)[/tex] for any [tex]\(x\)[/tex], the equation has infinitely many solutions.
(B) [tex]\(76x + 76 = -76x + 76\)[/tex]
1. Move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\(76x + 76x = 76 - 76\)[/tex]
2. Simplify:
[tex]\(152x = 0\)[/tex]
3. Divide both sides by 152:
[tex]\(x = 0\)[/tex]
Equation (B), like equation (A), also leads to [tex]\(x = 0\)[/tex] being a valid solution, but the structural form [tex]\(0 = 0\)[/tex] implies infinitely many solutions.
(C) [tex]\(-76x + 76 = -76x + 76\)[/tex]
1. The equation is already simplified, showing that both sides of the equation are equal regardless of [tex]\(x\)[/tex].
2. This essentially means it forms [tex]\(0 = 0\)[/tex], which is always true.
For equation (C), this condition implies that it has infinitely many solutions because any value of [tex]\(x\)[/tex] satisfies the equation.
(D) [tex]\(76x + 76 = 76x + 76\)[/tex]
1. Simplify both sides:
The equation essentially shows that the two sides are always equal.
2. This can be written as [tex]\(0 = 0\)[/tex], which is always true.
Thus, for equation (D), any value of [tex]\(x\)[/tex] will satisfy the equation, indicating infinitely many solutions.
In conclusion, all the given equations (A, B, C, and D) result in structural forms that hold true for any value of [tex]\(x\)[/tex], which means each one has infinitely many solutions.
(A) [tex]\(-76x + 76 = 76x + 76\)[/tex]
1. Start by moving all the terms involving [tex]\(x\)[/tex] to one side of the equation:
[tex]\(-76x - 76x = 76 - 76\)[/tex]
2. Combine like terms:
[tex]\(-152x = 0\)[/tex]
3. Divide both sides by [tex]\(-152\)[/tex]:
[tex]\(x = 0\)[/tex]
For equation (A), if you substitute [tex]\(x = 0\)[/tex], it satisfies the equation, indicating that [tex]\(x = 0\)[/tex] is a solution. Since the form suggests [tex]\(0 = 0\)[/tex] for any [tex]\(x\)[/tex], the equation has infinitely many solutions.
(B) [tex]\(76x + 76 = -76x + 76\)[/tex]
1. Move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\(76x + 76x = 76 - 76\)[/tex]
2. Simplify:
[tex]\(152x = 0\)[/tex]
3. Divide both sides by 152:
[tex]\(x = 0\)[/tex]
Equation (B), like equation (A), also leads to [tex]\(x = 0\)[/tex] being a valid solution, but the structural form [tex]\(0 = 0\)[/tex] implies infinitely many solutions.
(C) [tex]\(-76x + 76 = -76x + 76\)[/tex]
1. The equation is already simplified, showing that both sides of the equation are equal regardless of [tex]\(x\)[/tex].
2. This essentially means it forms [tex]\(0 = 0\)[/tex], which is always true.
For equation (C), this condition implies that it has infinitely many solutions because any value of [tex]\(x\)[/tex] satisfies the equation.
(D) [tex]\(76x + 76 = 76x + 76\)[/tex]
1. Simplify both sides:
The equation essentially shows that the two sides are always equal.
2. This can be written as [tex]\(0 = 0\)[/tex], which is always true.
Thus, for equation (D), any value of [tex]\(x\)[/tex] will satisfy the equation, indicating infinitely many solutions.
In conclusion, all the given equations (A, B, C, and D) result in structural forms that hold true for any value of [tex]\(x\)[/tex], which means each one has infinitely many solutions.
Thanks for taking the time to read Which of the following equations have infinitely many solutions Choose all answers that apply A tex 76x 76 76x 76 tex B tex 76x 76. 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