Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Determine whether the following equations have no solution, one solution, or infinitely many solutions:

1. [tex]\[-1.7v + 2.8 = 1.4v - 3.1v + 2.8\][/tex]

2. [tex]\[4a - 3 + 2a = 7a - 2\][/tex]

3. [tex]\[\frac{1}{5}f - \frac{2}{3} = -\frac{1}{5}f + \frac{2}{3}\][/tex]

4. [tex]\[2y - 3 = 5 + 2(y - 1)\][/tex]

5. [tex]\[-3(n + 4) + n = -2(n + 6)\][/tex]

Sagot :

GinnyAnswer
Let's solve each equation one by one to determine whether they have no solution, one solution, or infinitely many solutions.

### Equation 1:
[tex]\[ -1.7v + 2.8 = 1.4v - 3.1v + 2.8 \][/tex]

1. Combine like terms on the right-hand side:
[tex]\[ -1.7v + 2.8 = (1.4v - 3.1v) + 2.8 \][/tex]
[tex]\[ -1.7v + 2.8 = -1.7v + 2.8 \][/tex]

2. Subtract [tex]\(-1.7v + 2.8\)[/tex] from both sides:
[tex]\[ 0 = 0 \][/tex]

This equation simplifies to an identity [tex]\(0 = 0\)[/tex], which means it has infinitely many solutions.

### Equation 2:
[tex]\[ 4a - 3 + 2a = 7a - 2 \][/tex]

1. Combine like terms on the left-hand side:
[tex]\[ (4a + 2a) - 3 = 7a - 2 \][/tex]
[tex]\[ 6a - 3 = 7a - 2 \][/tex]

2. Subtract [tex]\(6a\)[/tex] from both sides:
[tex]\[ -3 = a - 2 \][/tex]

3. Add 2 to both sides:
[tex]\[ -1 = a \][/tex]

This equation has one solution, [tex]\(a = -1\)[/tex].

### Equation 3:
[tex]\[ \frac{1}{5}f - \frac{2}{3} = -\frac{1}{5}f + \frac{2}{3} \][/tex]

1. Combine like terms by adding [tex]\(\frac{1}{5}f\)[/tex] to both sides:
[tex]\[ \frac{1}{5}f + \frac{1}{5}f - \frac{2}{3} = \frac{2}{3} \][/tex]
[tex]\[ \frac{2}{5}f - \frac{-2}{3} = \frac{2}{3} \][/tex]

2. Add [tex]\(\frac{2}{3}\)[/tex] to both sides:
[tex]\[ \frac{2}{5}f = \frac{2}{3} + \frac{2}{3} \][/tex]
[tex]\[ \frac{2}{5} + \frac{2}{6} != \frac{1}{5} \][/tex]

This equation has no solution.

### Equation 4:
[tex]\[ 2y - 3 = 5 + 2(y - 1) \][/tex]

1. Distribute the 2 on the right-hand side:
[tex]\[ 2y - 3 = 5 + 2y - 2 \][/tex]

Combine like terms on the right-hand side:
[tex]\[ 2y - 3 = 2y + 3 \][/tex]

2. Subtract [tex]\(2y\)[/tex] from both sides:
[tex]\[ -3 = 3 \][/tex]

This is a contradiction, so the equation has no solution.

### Equation 5:
[tex]\[ -3(n + 4) + n = -2(n + 6) \][/tex]

1. Distribute the constants:
[tex]\[ -3n - 12 + n = -2n - 12 \][/tex]

2. Combine like terms on both sides:
[tex]\[ -2n - 12 = -2n - 12\][/tex]

Since both sides are equal, this equation has infinitely many solutions.

### Summary:

- Equation 1: Infinitely many solutions
- Equation 2: One solution [tex]\((a = -1)\)[/tex]
- Equation 3: No solution
- Equation 4: No solution
- Equation 5: Infinitely many solutions
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.