Question

Question
Order the steps for solving the equation: 2x−5=3(4x+5)



(8 points)
2x−5=3(4x+5)
Step 1:
Property to get


Step 2:
Property to get

Step 3:
Property to get

Step 4:
Property to get

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Answer 1

do it more clearly

Answer 2

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

1. **Step 1: Distribute on the right side of the equation.**
\[
2x - 5 = 12x + 15
\]
(This involves applying the distributive property: \( 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \))

2. **Step 2: Subtract \( 12x \) from both sides.**
\[
2x - 12x - 5 = 15
\]
(This involves combining like terms to isolate \( x \) on one side)

3. **Step 3: Combine like terms.**
\[
-10x - 5 = 15
\]

4. **Step 4: Add 5 to both sides.**
\[
-10x = 20
\]

5. **Step 5: Divide by -10.**
\[
x = -2
\]

So the completed ordered steps for the equation \( 2x - 5 = 3(4x + 5) \) are:

- Step 1: Distribute on the right side of the equation.
- Step 2: Subtract \( 12x \) from both sides.
- Step 3: Combine like terms on the left side.
- Step 4: Add 5 to both sides.
- Step 5: Divide by -10 to solve for \( x \).

Your output should reflect the step-wise approach to arriving at the solution.

Answer 3

Sure! Let's clearly outline the steps to solve the equation \( 2x - 5 = 3(4x + 5) \) in a more structured way:

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

**Step 1: Distribute**
- Apply the distributive property to the right side of the equation.
- Rewrite the equation:
\[
2x - 5 = 3 \cdot 4x + 3 \cdot 5
\]
This results in:
\[
2x - 5 = 12x + 15
\]

**Step 2: Move all \( x \) terms to one side**
- Subtract \( 12x \) from both sides:
\[
2x - 12x - 5 = 15
\]
This simplifies to:
\[
-10x - 5 = 15
\]

**Step 3: Move constant terms to the other side**
- Add \( 5 \) to both sides:
\[
-10x - 5 + 5 = 15 + 5
\]
This simplifies to:
\[
-10x = 20
\]

**Step 4: Solve for \( x \)**
- Divide both sides by -10:
\[
x = \frac{20}{-10}
\]
Which simplifies to:
\[
x = -2
\]

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

This structured format clearly walks through each step in a logical sequence.