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

1 answer

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:

\[ \boxed{-2} \]