Question

what are the steps to solving the equation: 2x-5=3(4x+5)

Answer 1

thats not one of the answer choices, its subtraction of equality, distributive, addition of equality, combine like terms, division of equality. its a multi-step question, when you pick one of these questions you have more to go

:))

Answer 2

step 2 & 3 are wrong, the math vocabulary you used is not an answer choice sadly.

Answer 3

again, step two and three are wrong.
step 2's choices are: distributive, addition of equality, combine like terms, division of equality
three is: its subtraction of equality, distributive, combine like terms, division of equality.

Answer 4

To solve the equation \( 2x - 5 = 3(4x + 5) \), follow these steps:

1. **Distribute the \( 3 \)** on the right side:
\[
2x - 5 = 3 \cdot 4x + 3 \cdot 5
\]
\[
2x - 5 = 12x + 15
\]

2. **Rearrange the equation** to get all terms involving \( x \) on one side and constant terms on the other side. We can do this by subtracting \( 12x \) from both sides:
\[
2x - 12x - 5 = 15
\]
\[
-10x - 5 = 15
\]

3. **Add \( 5 \)** to both sides to isolate terms involving \( x \):
\[
-10x - 5 + 5 = 15 + 5
\]
\[
-10x = 20
\]

4. **Divide both sides by \(-10\)** to solve for \( x \):
\[
x = \frac{20}{-10}
\]
\[
x = -2
\]

5. **Check your solution** by substituting \( x = -2 \) back into the original equation:
\[
2(-2) - 5 = 3(4(-2) + 5)
\]
\[
-4 - 5 = 3(-8 + 5)
\]
\[
-9 = 3(-3)
\]
\[
-9 = -9
\]
The left side equals the right side, confirming that \( x = -2 \) is indeed the correct solution.

Thus, the solution to the equation \( 2x - 5 = 3(4x + 5) \) is:
\[
\boxed{-2}
\]

Answer 5

It sounds like you're looking for a more structured outline of the solving process using specific steps. Let's break it down according to the terms you provided: **subtraction of equality, distributive, addition of equality, combine like terms, and division of equality.**

### Steps to Solve the Equation \( 2x - 5 = 3(4x + 5) \)

1. **Distributive**:
Start with the original equation:
\[
2x - 5 = 3(4x + 5)
\]
Use the distributive property on the right side:
\[
2x - 5 = 12x + 15
\]

2. **Subtraction of Equality**:
Subtract \( 12x \) from both sides to get all \( x \) terms on one side:
\[
2x - 12x - 5 = 15
\]
This simplifies to:
\[
-10x - 5 = 15
\]

3. **Addition of Equality**:
Add \( 5 \) to both sides to isolate the terms involving \( x \):
\[
-10x - 5 + 5 = 15 + 5
\]
Which simplifies to:
\[
-10x = 20
\]

4. **Division of Equality**:
Divide both sides by \(-10\) to solve for \( x \):
\[
x = \frac{20}{-10}
\]
Thus, we find:
\[
x = -2
\]

5. **Combine Like Terms**:
Although we already combined like terms in previous steps, note that this is implicit in our operations. If necessary, you could explicitly show that we already combined \( -10x \) (from \( 2x - 12x \)) in the process.

### Final Result
The solution to the equation \( 2x - 5 = 3(4x + 5) \) is:
\[
\boxed{-2}
\]

### Multi-step Process
This outline sequentially conforms to the steps you provided: **distributive**, **subtraction of equality**, **addition of equality**, **combining like terms**, and **division of equality**. Each operation builds toward finding the solution \( x = -2 \). If you have specific choices or options to select from, these terminologies should align with that format. Thank you for your clarification!

Answer 6

I understand now that you are looking for the solution steps laid out according to specific mathematical vocabulary rather than descriptions. Let’s outline the solution to the equation \( 2x - 5 = 3(4x + 5) \) using the terms you specified:

### Given Equation:
\[
2x - 5 = 3(4x + 5)
\]

### Step 1: **Distributive**
Distribute \( 3 \) on the right side:
\[
2x - 5 = 12x + 15
\]

### Step 2: **Subtraction of Equality**
Subtract \( 12x \) from both sides:
\[
2x - 12x - 5 = 15
\]
This simplifies to:
\[
-10x - 5 = 15
\]

### Step 3: **Addition of Equality**
Add \( 5 \) to both sides:
\[
-10x - 5 + 5 = 15 + 5
\]
This results in:
\[
-10x = 20
\]

### Step 4: **Division of Equality**
Divide both sides by \(-10\):
\[
x = \frac{20}{-10}
\]
Thus, we have:
\[
x = -2
\]

### Step 5: **Combine Like Terms**
This step is implicitly done when subtracting and adding, as well as during the initial distribution. It confirms that on each step, similar terms are grouped accurately.

### Conclusion
The solution to the equation is:
\[
\boxed{-2}
\]

These steps are now aligned with the specific vocabulary you provided. If you have any other questions or need further clarification, feel free to ask!

Answer 7

Thank you for your patience, and I appreciate your clarification regarding the vocabulary and the specific choices for each step. Let's solve the equation \( 2x - 5 = 3(4x + 5) \) and select the correct vocabulary steps according to your specifications.

### Given Equation:
\[
2x - 5 = 3(4x + 5)
\]

### Step 1: **Distributive**
Distributing \( 3 \) on the right side:
\[
2x - 5 = 12x + 15
\]

### Step 2: **Combine Like Terms**
We will move \( 12x \) to the left side to combine like terms. This represents moving terms involving \( x \):
\[
2x - 12x - 5 = 15
\]
This simplifies to:
\[
-10x - 5 = 15
\]

### Step 3: **Addition of Equality**
Now, we will add \( 5 \) to both sides to eliminate the constant on the left side:
\[
-10x - 5 + 5 = 15 + 5
\]
This results in:
\[
-10x = 20
\]

### Step 4: **Division of Equality**
Finally, we will divide both sides by \(-10\) to solve for \( x \):
\[
x = \frac{20}{-10}
\]
Thus, we have:
\[
x = -2
\]

### Summary of Steps
1. **Distributive** (Step 1)
2. **Combine Like Terms** (Step 2)
3. **Addition of Equality** (Step 3)
4. **Division of Equality** (Step 4)

The final solution to the equation is:
\[
\boxed{-2}
\]

Thank you for highlighting the correct choices for each step! If there are any more adjustments needed, please let me know.