Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Certainly! Let's go through each of the given equations step-by-step to determine the solution type: one solution, infinitely many solutions, or no solution.
### 1. Equation: \( 5(x-2) = 5x - 7 \)
Let's expand and simplify both sides:
[tex]\[ 5(x - 2) = 5x - 10 \][/tex]
The equation now is:
[tex]\[ 5x - 10 = 5x - 7 \][/tex]
Subtract \( 5x \) from both sides:
[tex]\[ -10 = -7 \][/tex]
This is a contradiction. Therefore, this equation has No Solution.
### 2. Equation: \( -3(x-4) = -3x + 12 \)
Let's expand and simplify both sides:
[tex]\[ -3(x - 4) = -3x + 12 \][/tex]
[tex]\[ -3x + 12 = -3x + 12 \][/tex]
Both sides are identical. Therefore, this equation has Infinitely Many Solutions.
### 3. Equation: \( 4(x+1) = 3x + 4 \)
Let's expand and simplify both sides:
[tex]\[ 4(x + 1) = 4x + 4 \][/tex]
Now, the equation is:
[tex]\[ 4x + 4 = 3x + 4 \][/tex]
Subtract \( 3x \) from both sides:
[tex]\[ x + 4 = 4 \][/tex]
Subtract 4 from both sides:
[tex]\[ x = 0 \][/tex]
So, this equation has One Solution.
### 4. Equation: \( -2(x-3) = 2x - 6 \)
Let's expand and simplify both sides:
[tex]\[ -2(x - 3) = -2x + 6 \][/tex]
The equation now is:
[tex]\[ -2x + 6 = 2x - 6 \][/tex]
Add \( 2x \) to both sides:
[tex]\[ 6 = 4x - 6 \][/tex]
Add 6 to both sides:
[tex]\[ 12 = 4x \][/tex]
Divide by 4:
[tex]\[ x = 3 \][/tex]
So, this equation has One Solution.
### 5. Equation: \( 6(x+5) = 6x + 11 \)
Let's expand and simplify both sides:
[tex]\[ 6(x + 5) = 6x + 30 \][/tex]
The equation now is:
[tex]\[ 6x + 30 = 6x + 11 \][/tex]
Subtract \( 6x \) from both sides:
[tex]\[ 30 = 11 \][/tex]
This is a contradiction. Therefore, this equation has No Solution.
### Summary
Let's sort the equations based on their solutions:
- Infinitely Many Solutions:
- \( -3(x-4) = -3x + 12 \)
- No Solution:
- \( 5(x-2) = 5x - 7 \)
- \( 6(x+5) = 6x + 11 \)
- One Solution:
- \( 4(x+1) = 3x + 4 \)
- [tex]\( -2(x-3) = 2x - 6 \)[/tex]
### 1. Equation: \( 5(x-2) = 5x - 7 \)
Let's expand and simplify both sides:
[tex]\[ 5(x - 2) = 5x - 10 \][/tex]
The equation now is:
[tex]\[ 5x - 10 = 5x - 7 \][/tex]
Subtract \( 5x \) from both sides:
[tex]\[ -10 = -7 \][/tex]
This is a contradiction. Therefore, this equation has No Solution.
### 2. Equation: \( -3(x-4) = -3x + 12 \)
Let's expand and simplify both sides:
[tex]\[ -3(x - 4) = -3x + 12 \][/tex]
[tex]\[ -3x + 12 = -3x + 12 \][/tex]
Both sides are identical. Therefore, this equation has Infinitely Many Solutions.
### 3. Equation: \( 4(x+1) = 3x + 4 \)
Let's expand and simplify both sides:
[tex]\[ 4(x + 1) = 4x + 4 \][/tex]
Now, the equation is:
[tex]\[ 4x + 4 = 3x + 4 \][/tex]
Subtract \( 3x \) from both sides:
[tex]\[ x + 4 = 4 \][/tex]
Subtract 4 from both sides:
[tex]\[ x = 0 \][/tex]
So, this equation has One Solution.
### 4. Equation: \( -2(x-3) = 2x - 6 \)
Let's expand and simplify both sides:
[tex]\[ -2(x - 3) = -2x + 6 \][/tex]
The equation now is:
[tex]\[ -2x + 6 = 2x - 6 \][/tex]
Add \( 2x \) to both sides:
[tex]\[ 6 = 4x - 6 \][/tex]
Add 6 to both sides:
[tex]\[ 12 = 4x \][/tex]
Divide by 4:
[tex]\[ x = 3 \][/tex]
So, this equation has One Solution.
### 5. Equation: \( 6(x+5) = 6x + 11 \)
Let's expand and simplify both sides:
[tex]\[ 6(x + 5) = 6x + 30 \][/tex]
The equation now is:
[tex]\[ 6x + 30 = 6x + 11 \][/tex]
Subtract \( 6x \) from both sides:
[tex]\[ 30 = 11 \][/tex]
This is a contradiction. Therefore, this equation has No Solution.
### Summary
Let's sort the equations based on their solutions:
- Infinitely Many Solutions:
- \( -3(x-4) = -3x + 12 \)
- No Solution:
- \( 5(x-2) = 5x - 7 \)
- \( 6(x+5) = 6x + 11 \)
- One Solution:
- \( 4(x+1) = 3x + 4 \)
- [tex]\( -2(x-3) = 2x - 6 \)[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.