Question
Solve the equation. Please show the process to solve.
2x + 3 = 2x +7
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
7x + 3 = 7x + 3
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
4x + 22 = 8× + 10
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
5× + 5 = 5× + 4
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
3x + 18 = 5× + 8
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
3(4x + 8) = 4(3x + 6)
How many solutions does this equation have? Circle below.
None
One
Infinite
2x + 3 = 2x +7
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
7x + 3 = 7x + 3
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
4x + 22 = 8× + 10
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
5× + 5 = 5× + 4
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
3x + 18 = 5× + 8
How many solutions does this equation have? Circle below.
None
One
Infinite
Solve the equation. Please show the process to solve.
3(4x + 8) = 4(3x + 6)
How many solutions does this equation have? Circle below.
None
One
Infinite
Answers
There are no human answers yet.
Answered by
GPT-4o mini
Let’s solve each of the equations step by step and determine how many solutions each has.
### 1. Equation: \( 2x + 3 = 2x + 7 \)
**Step 1:** Subtract \( 2x \) from both sides:
\[
2x + 3 - 2x = 2x + 7 - 2x \\
3 = 7
\]
This is not true (3 does not equal 7).
**Conclusion:** There are **None** solutions.
---
### 2. Equation: \( 7x + 3 = 7x + 3 \)
**Step 1:** Subtract \( 7x \) from both sides:
\[
7x + 3 - 7x = 7x + 3 - 7x \\
3 = 3
\]
This is always true.
**Conclusion:** There are **Infinite** solutions.
---
### 3. Equation: \( 4x + 22 = 8x + 10 \)
**Step 1:** Subtract \( 4x \) from both sides:
\[
4x + 22 - 4x = 8x + 10 - 4x \\
22 = 4x + 10
\]
**Step 2:** Subtract 10 from both sides:
\[
22 - 10 = 4x \\
12 = 4x
\]
**Step 3:** Divide both sides by 4:
\[
x = 3
\]
**Conclusion:** There is **One** solution.
---
### 4. Equation: \( 5x + 5 = 5x + 4 \)
**Step 1:** Subtract \( 5x \) from both sides:
\[
5x + 5 - 5x = 5x + 4 - 5x \\
5 = 4
\]
This is not true (5 does not equal 4).
**Conclusion:** There are **None** solutions.
---
### 5. Equation: \( 3x + 18 = 5x + 8 \)
**Step 1:** Subtract \( 3x \) from both sides:
\[
3x + 18 - 3x = 5x + 8 - 3x \\
18 = 2x + 8
\]
**Step 2:** Subtract 8 from both sides:
\[
18 - 8 = 2x \\
10 = 2x
\]
**Step 3:** Divide both sides by 2:
\[
x = 5
\]
**Conclusion:** There is **One** solution.
---
### 6. Equation: \( 3(4x + 8) = 4(3x + 6) \)
**Step 1:** Distribute both sides:
\[
12x + 24 = 12x + 24
\]
**Step 2:** Subtract \( 12x \) from both sides:
\[
12x + 24 - 12x = 12x + 24 - 12x \\
24 = 24
\]
This is always true.
**Conclusion:** There are **Infinite** solutions.
---
### Summary of Solutions
1. \( 2x + 3 = 2x + 7 \) - **None**
2. \( 7x + 3 = 7x + 3 \) - **Infinite**
3. \( 4x + 22 = 8x + 10 \) - **One**
4. \( 5x + 5 = 5x + 4 \) - **None**
5. \( 3x + 18 = 5x + 8 \) - **One**
6. \( 3(4x + 8) = 4(3x + 6) \) - **Infinite**
### 1. Equation: \( 2x + 3 = 2x + 7 \)
**Step 1:** Subtract \( 2x \) from both sides:
\[
2x + 3 - 2x = 2x + 7 - 2x \\
3 = 7
\]
This is not true (3 does not equal 7).
**Conclusion:** There are **None** solutions.
---
### 2. Equation: \( 7x + 3 = 7x + 3 \)
**Step 1:** Subtract \( 7x \) from both sides:
\[
7x + 3 - 7x = 7x + 3 - 7x \\
3 = 3
\]
This is always true.
**Conclusion:** There are **Infinite** solutions.
---
### 3. Equation: \( 4x + 22 = 8x + 10 \)
**Step 1:** Subtract \( 4x \) from both sides:
\[
4x + 22 - 4x = 8x + 10 - 4x \\
22 = 4x + 10
\]
**Step 2:** Subtract 10 from both sides:
\[
22 - 10 = 4x \\
12 = 4x
\]
**Step 3:** Divide both sides by 4:
\[
x = 3
\]
**Conclusion:** There is **One** solution.
---
### 4. Equation: \( 5x + 5 = 5x + 4 \)
**Step 1:** Subtract \( 5x \) from both sides:
\[
5x + 5 - 5x = 5x + 4 - 5x \\
5 = 4
\]
This is not true (5 does not equal 4).
**Conclusion:** There are **None** solutions.
---
### 5. Equation: \( 3x + 18 = 5x + 8 \)
**Step 1:** Subtract \( 3x \) from both sides:
\[
3x + 18 - 3x = 5x + 8 - 3x \\
18 = 2x + 8
\]
**Step 2:** Subtract 8 from both sides:
\[
18 - 8 = 2x \\
10 = 2x
\]
**Step 3:** Divide both sides by 2:
\[
x = 5
\]
**Conclusion:** There is **One** solution.
---
### 6. Equation: \( 3(4x + 8) = 4(3x + 6) \)
**Step 1:** Distribute both sides:
\[
12x + 24 = 12x + 24
\]
**Step 2:** Subtract \( 12x \) from both sides:
\[
12x + 24 - 12x = 12x + 24 - 12x \\
24 = 24
\]
This is always true.
**Conclusion:** There are **Infinite** solutions.
---
### Summary of Solutions
1. \( 2x + 3 = 2x + 7 \) - **None**
2. \( 7x + 3 = 7x + 3 \) - **Infinite**
3. \( 4x + 22 = 8x + 10 \) - **One**
4. \( 5x + 5 = 5x + 4 \) - **None**
5. \( 3x + 18 = 5x + 8 \) - **One**
6. \( 3(4x + 8) = 4(3x + 6) \) - **Infinite**
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