Question

2x - 5 = 3(4x +5) solve the following equation write out all your work for all steps to solve the equation

Answer 1

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

### Step 1: Distribute the right side of the equation
First, we need to distribute the \(3\) on the right-hand side:

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

So, the equation now looks like:

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

### Step 2: Move all terms involving \(x\) to one side
We can move \(12x\) to the left-hand side by subtracting \(12x\) from both sides:

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

This simplifies to:

\[
-10x - 5 = 15
\]

### Step 3: Move constant terms to the other side
Next, we want to isolate the terms with \(x\). We can do this by adding \(5\) to both sides:

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

This simplifies to:

\[
-10x = 20
\]

### Step 4: Solve for \(x\)
Now we will 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:

\[
\boxed{-2}
\]