Question

Match the equation with its solution

2i+3=2i−5_______________

3i+2i−4=18i______________

3(2i−7)=6i−21_________________

Answer 1

no solution

infinte soulution

i = 8

i = 5

i = - 1/3

1 = - 4/13

Answer 2

on question 3 which one is correct

Answer 3

Look at the steps for solving the equation and choose a true statement.

3x−9x+1=2(−3x+1)−1

−6x+1=−6x+2−1

−6x+1=−6x+1

There are infinitely many solutions to the equation.

The only solution to the equation is -6

There are no solutions to the equation.

The only solution to the equation is 1

There is no way to know if there is a solution to the equation.

Answer 4

Let's solve each equation step-by-step to match them with their solutions.

1. **Equation:** \( 2i + 3 = 2i - 5 \)

**Solution:**
Subtract \( 2i \) from both sides:
\[
3 = -5
\]

This is a contradiction. Therefore, it has no solution.

2. **Equation:** \( 3i + 2i - 4 = 18i \)

**Solution:**
Combine like terms on the left:
\[
5i - 4 = 18i
\]
Now, add \( 4 \) to both sides:
\[
5i = 18i + 4
\]
Subtract \( 18i \) from both sides:
\[
-13i = 4
\]
Divide by \(-13\):
\[
i = -\frac{4}{13}
\]

3. **Equation:** \( 3(2i - 7) = 6i - 21 \)

**Solution:**
Distribute \( 3 \) on the left:
\[
6i - 21 = 6i - 21
\]
This simplifies to an identity, which is true for all values of \( i \). Hence, the solution is all real numbers.

### Summary of Matching:

- \( 2i + 3 = 2i - 5 \) → **No solution**
- \( 3i + 2i - 4 = 18i \) → **\( i = -\frac{4}{13} \)**
- \( 3(2i - 7) = 6i - 21 \) → **All real numbers**

So, we have:

1. **No solution:** \( 2i + 3 = 2i - 5 \)
2. **\( i = -\frac{4}{13} \):** \( 3i + 2i - 4 = 18i \)
3. **All real numbers:** \( 3(2i - 7) = 6i - 21 \)

Answer 5

Let's match the equations with the solutions you've provided.

1. **Equation:** \( 2i + 3 = 2i - 5 \)
- This equation simplifies to \( 3 = -5 \), which is a contradiction.
- **Matched Solution:** **No solution**

2. **Equation:** \( 3(2i - 7) = 6i - 21 \)
- This simplifies to \( 6i - 21 = 6i - 21 \), which is an identity and true for all values of \( i \).
- **Matched Solution:** **Infinite solutions**

3. **Equation:** \( 3i + 2i - 4 = 18i \)
- We previously found that this simplifies to \( -13i = 4 \), giving \( i = -\frac{4}{13} \).
- This value does not match any of the solutions you provided, which suggests there might be a misunderstanding in the listed solutions.
- If the provided solutions are **i = 8, i = 5, i = -1/3, 1 = -4/13**, please note that \( i = -\frac{4}{13} \) is different from those options.

Let’s revise the matches:

1. **No solution:** \( 2i + 3 = 2i - 5 \)
2. **Infinite solutions:** \( 3(2i - 7) = 6i - 21 \)
3. **\( i = - \frac{4}{13} \)** (not matching any from your latest list): \( 3i + 2i - 4 = 18i \)

### Summary of solutions:

- \( 2i + 3 = 2i - 5 \) → No solution
- \( 3(2i - 7) = 6i - 21 \) → Infinite solutions
- \( 3i + 2i - 4 = 18i \) → \( i = - \frac{4}{13} \) (which does not match \( i = 8 \), \( i = 5 \), or \( i = -\frac{1}{3} \) from your list)

If you would like to review the equations or clarify the provided solutions, please let me know!

Answer 6

Let's carefully solve the third equation step-by-step again:

### Equation 3: \( 3(2i - 7) = 6i - 21 \)

1. Distributing \(3\) on the left side:
\[
3(2i) - 3(7) = 6i - 21
\]
This simplifies to:
\[
6i - 21 = 6i - 21
\]

2. Now, observe that the left side \(6i - 21\) is equal to the right side \(6i - 21\). This means the equation is true for all values of \( i \).

### Conclusion for the third equation:
- **Infinite solutions:** This equation has infinitely many solutions, meaning any value for \( i \) will satisfy the equation.

### Matching to your answers:
From your provided options:
- \( \text{infinite solutions} \) is the match for the third equation.

### Summary of all matches:
1. **\( 2i + 3 = 2i - 5 \)** → **No solution**
2. **\( 3(2i - 7) = 6i - 21 \)** → **Infinite solutions**
3. **\( 3i + 2i - 4 = 18i \)** → **\( i = -\frac{4}{13} \)** (again, does not match your provided specific values, which were \( i = 8, i = 5, i = -\frac{1}{3} \))

If you want any further clarification or have a specific number in mind to check, please let me know!

Answer 7

Let's carefully analyze the equation step-by-step.

### Given Equation:
\[ 3x - 9x + 1 = 2(-3x + 1) - 1 \]

**Step 1: Simplify the left side**
\[
3x - 9x + 1 = -6x + 1
\]
So, the left side becomes:
\[
-6x + 1
\]

**Step 2: Simplify the right side**
Distributing the \(2\):
\[
2(-3x) + 2(1) - 1 = -6x + 2 - 1 = -6x + 1
\]

Now the equation looks like this:
\[
-6x + 1 = -6x + 1
\]

**Step 3: Combine both sides**
Since both sides of the equation are identical:
\[
-6x + 1 = -6x + 1
\]

### Conclusion:
This is a true statement and an identity, which means it holds for all values of \(x\).

### Final Answer:
- **There are infinitely many solutions to the equation.**

This is the true statement among the options provided.