At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
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
### 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
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.