Answered

IDNLearn.com makes it easy to get reliable answers from experts and enthusiasts alike. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

Which of the following equations have exactly one solution? Choose all answers that apply:

A. [tex]12x + 12 = 13x - 12[/tex]

B. [tex]-13x + 12 = 13x + 13[/tex]

C. [tex]-13x + 12 = 13x - 13[/tex]

D. [tex]12x + 12 = 13x + 12[/tex]

Sagot :

GinnyAnsweridn
Let's analyze each of the given equations to determine which ones have exactly one solution.

### Equation (A)
[tex]\[ 12x + 12 = 13x - 12 \][/tex]

First, we'll isolate [tex]\(x\)[/tex] by moving all terms involving [tex]\(x\)[/tex] to one side and the constant terms to the other side:

[tex]\[ 12x + 12 = 13x - 12 \][/tex]

Subtract [tex]\(12x\)[/tex] from both sides:

[tex]\[ 12 = x - 12 \][/tex]

Add 12 to both sides:

[tex]\[ 24 = x \][/tex]

Therefore, equation (A) has exactly one solution, [tex]\(x = 24\)[/tex].

### Equation (B)
[tex]\[ -13x + 12 = 13x + 13 \][/tex]

Again, we'll isolate [tex]\(x\)[/tex] by moving all terms involving [tex]\(x\)[/tex] to one side and the constant terms to the other side:

[tex]\[ -13x + 12 = 13x + 13 \][/tex]

Add [tex]\(13x\)[/tex] to both sides:

[tex]\[ 12 = 26x + 13 \][/tex]

Subtract 13 from both sides:

[tex]\[ -1 = 26x \][/tex]

Divide both sides by 26:

[tex]\[ x = -\frac{1}{26} \][/tex]

Therefore, equation (B) has exactly one solution, [tex]\(x = -\frac{1}{26}\)[/tex].

### Equation (C)
[tex]\[ -13x + 12 = 13x - 13 \][/tex]

Isolating [tex]\(x\)[/tex], move all terms involving [tex]\(x\)[/tex] to one side and the constants to the other side:

[tex]\[ -13x + 12 = 13x - 13 \][/tex]

Add [tex]\(13x\)[/tex] to both sides:

[tex]\[ 12 = 26x - 13 \][/tex]

Add 13 to both sides:

[tex]\[ 25 = 26x \][/tex]

Divide both sides by 26:

[tex]\[ x = \frac{25}{26} \][/tex]

Therefore, equation (C) has exactly one solution, [tex]\(x = \frac{25}{26}\)[/tex].

### Equation (D)
[tex]\[ 12x + 12 = 13x + 12 \][/tex]

Isolating [tex]\(x\)[/tex], move all terms involving [tex]\(x\)[/tex] to one side and the constants to the other side:

[tex]\[ 12x + 12 = 13x + 12 \][/tex]

Subtract [tex]\(12x\)[/tex] from both sides:

[tex]\[ 12 = x + 12 \][/tex]

Subtract 12 from both sides:

[tex]\[ 0 = x \][/tex]

Therefore, equation (D) has exactly one solution, [tex]\(x = 0\)[/tex].

### Conclusion
Upon reviewing the calculations, it is evident that each of the equations (A), (B), (C), and (D) has exactly one solution.
So, the correct answer is:
- (A)
- (B)
- (C)
- (D)
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.