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
Answer

Solve for the given variable.



8x+17=4x+58x+17=4x+58x+17=4x+5



x=x=x=
Answer

Solve the following linear equation.



−2y+4=20-2y+4=20−2y+4=20



y=y=y=
Answer
Solve for the given variable.



−16z−17=−12z+5-16z-17=-12z+5−16z−17=−12z+5



z=z=z=
Answered by 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**
Answered by 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!
Answered by 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 \( y = -8 \).
Answered by 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:
\[
z = -\frac{11}{2} \quad \text{or} \quad z = -5.5
\]