Question
Consider the left side of the equation as
Match the right side of the equation to the indicated number of solutions.
Zero Solutions
One Solution
Infinite Solutions
Drag & Drop the answer
10x+1710x+1710x+17
10x+1810x+1810x+18
17x+1817x+1817x+18
Match the right side of the equation to the indicated number of solutions.
Zero Solutions
One Solution
Infinite Solutions
Drag & Drop the answer
10x+1710x+1710x+17
10x+1810x+1810x+18
17x+1817x+1817x+18
Answers
GPT-4o mini
To determine how many solutions each equation has, we need to analyze the left and right sides.
1. **10x + 17 = 10x + 17**
- This simplifies to \(0 = 0\), which means both sides are always equal for any value of \(x\).
- **Infinite Solutions**
2. **10x + 17 = 10x + 18**
- This simplifies to \(0 = 1\), which is a contradiction.
- **Zero Solutions**
3. **17x + 18 = 17x + 18**
- This simplifies also to \(0 = 0\), which is true for any \(x\).
- **Infinite Solutions**
Now we can match them:
- **Zero Solutions:** 10x + 17 = 10x + 18
- **One Solution:** (No equation matches this category.)
- **Infinite Solutions:** 10x + 17 = 10x + 17 and 17x + 18 = 17x + 18
So the final match result is:
- Zero Solutions: **10x + 18**
- One Solution: **(none)**
- Infinite Solutions: **10x + 17** and **17x + 18**
1. **10x + 17 = 10x + 17**
- This simplifies to \(0 = 0\), which means both sides are always equal for any value of \(x\).
- **Infinite Solutions**
2. **10x + 17 = 10x + 18**
- This simplifies to \(0 = 1\), which is a contradiction.
- **Zero Solutions**
3. **17x + 18 = 17x + 18**
- This simplifies also to \(0 = 0\), which is true for any \(x\).
- **Infinite Solutions**
Now we can match them:
- **Zero Solutions:** 10x + 17 = 10x + 18
- **One Solution:** (No equation matches this category.)
- **Infinite Solutions:** 10x + 17 = 10x + 17 and 17x + 18 = 17x + 18
So the final match result is:
- Zero Solutions: **10x + 18**
- One Solution: **(none)**
- Infinite Solutions: **10x + 17** and **17x + 18**
Solve for the given variable.
8x+17=4x+58x+17=4x+58x+17=4x+5
x=x=x=
GPT-4o mini
To solve for \( x \) in the equation \( 8x + 17 = 4x + 5 \), let's go through the steps:
1. Start with the equation:
\[
8x + 17 = 4x + 5
\]
2. Subtract \( 4x \) from both sides to get:
\[
8x - 4x + 17 = 5
\]
This simplifies to:
\[
4x + 17 = 5
\]
3. Next, subtract \( 17 \) from both sides:
\[
4x = 5 - 17
\]
This simplifies to:
\[
4x = -12
\]
4. Finally, divide both sides by \( 4 \):
\[
x = -3
\]
So, \( x = -3 \).
If you have additional equations or variables to solve, please provide them, and I'll be happy to assist!
1. Start with the equation:
\[
8x + 17 = 4x + 5
\]
2. Subtract \( 4x \) from both sides to get:
\[
8x - 4x + 17 = 5
\]
This simplifies to:
\[
4x + 17 = 5
\]
3. Next, subtract \( 17 \) from both sides:
\[
4x = 5 - 17
\]
This simplifies to:
\[
4x = -12
\]
4. Finally, divide both sides by \( 4 \):
\[
x = -3
\]
So, \( x = -3 \).
If you have additional equations or variables to solve, please provide them, and I'll be happy to assist!
Solve the following linear equation.
−2y+4=20-2y+4=20−2y+4=20
y=y=y=
GPT-4o mini
To solve the equation \(-2y + 4 = 20\), let's follow these steps:
1. Start with the equation:
\[
-2y + 4 = 20
\]
2. Subtract \(4\) from both sides:
\[
-2y = 20 - 4
\]
This simplifies to:
\[
-2y = 16
\]
3. Now, divide both sides by \(-2\):
\[
y = \frac{16}{-2}
\]
This gives:
\[
y = -8
\]
So, the solution is \( y = -8 \).
1. Start with the equation:
\[
-2y + 4 = 20
\]
2. Subtract \(4\) from both sides:
\[
-2y = 20 - 4
\]
This simplifies to:
\[
-2y = 16
\]
3. Now, divide both sides by \(-2\):
\[
y = \frac{16}{-2}
\]
This gives:
\[
y = -8
\]
So, the solution is \( y = -8 \).
Solve for the given variable.
−16z−17=−12z+5-16z-17=-12z+5−16z−17=−12z+5
z=z=z=
−16z−17=−12z+5-16z-17=-12z+5−16z−17=−12z+5
z=z=z=
GPT-4o mini
To solve the equation \( -16z - 17 = -12z + 5 \), let's follow these steps:
1. Start with the given equation:
\[
-16z - 17 = -12z + 5
\]
2. First, add \( 16z \) to both sides to eliminate the \( -16z \) on the left:
\[
-17 = 4z + 5
\]
3. Next, subtract \( 5 \) from both sides:
\[
-17 - 5 = 4z
\]
This simplifies to:
\[
-22 = 4z
\]
4. Finally, divide both sides by \( 4 \):
\[
z = \frac{-22}{4}
\]
Simplifying this, we get:
\[
z = -\frac{11}{2} \quad \text{or} \quad z = -5.5
\]
So, the solution is:
\[
z = -\frac{11}{2} \quad \text{or} \quad z = -5.5
\]
1. Start with the given equation:
\[
-16z - 17 = -12z + 5
\]
2. First, add \( 16z \) to both sides to eliminate the \( -16z \) on the left:
\[
-17 = 4z + 5
\]
3. Next, subtract \( 5 \) from both sides:
\[
-17 - 5 = 4z
\]
This simplifies to:
\[
-22 = 4z
\]
4. Finally, divide both sides by \( 4 \):
\[
z = \frac{-22}{4}
\]
Simplifying this, we get:
\[
z = -\frac{11}{2} \quad \text{or} \quad z = -5.5
\]
So, the solution is:
\[
z = -\frac{11}{2} \quad \text{or} \quad z = -5.5
\]