Question

Use the following step as a guide to solve the following equation. Write out your work for all steps to solve the equation.

2x - 5 = 3(4x + 5)

Step 1. Distributive Property

Step 2. move variables to one side of the equation

Step 3.move constant to the other side of the equation

Step 4. isolate your variable

Answer 1

make it way more short and simple

Answer 2

Let's solve the equation \( 2x - 5 = 3(4x + 5) \) following the provided steps.

### Step 1: Distributive Property
First, we need to apply the distributive property on the right side of the equation:

\[
3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15
\]

Now, we can rewrite the equation as:

\[
2x - 5 = 12x + 15
\]

### Step 2: Move Variables to One Side of the Equation
Next, we will move the variable terms to one side. We can subtract \(12x\) from both sides of the equation:

\[
2x - 12x - 5 = 15
\]

Combine like terms:

\[
-10x - 5 = 15
\]

### Step 3: Move Constant to the Other Side of the Equation
Now, we want to move the constant term (-5) to the other side. To do this, we add 5 to both sides of the equation:

\[
-10x - 5 + 5 = 15 + 5
\]

This simplifies to:

\[
-10x = 20
\]

### Step 4: Isolate Your Variable
Finally, we will isolate the variable \(x\). To do this, we divide both sides by -10:

\[
x = \frac{20}{-10}
\]

This simplifies to:

\[
x = -2
\]

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

\[
\boxed{-2}
\]

Answer 3

Sure! Here’s a more concise solution to the equation \( 2x - 5 = 3(4x + 5) \).

### Step 1: Distributive Property
Expand the right side:

\[
2x - 5 = 12x + 15
\]

### Step 2: Move Variables to One Side
Subtract \(12x\) from both sides:

\[
2x - 12x - 5 = 15 \implies -10x - 5 = 15
\]

### Step 3: Move Constant to the Other Side
Add 5 to both sides:

\[
-10x = 20
\]

### Step 4: Isolate Your Variable
Divide by -10:

\[
x = -2
\]

### Final Answer
The solution is:

\[
\boxed{-2}
\]