Use the following step as a guide to solve the following equationWrite out your work for all steps to solve the equation . 2x - 5 = 3(4x + 5)

Answer 1

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

Step 1: Expand the right side

First, we need to distribute the 3 on the right side of the equation:

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

Now we can rewrite the equation:

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

Step 2: Move all terms involving \( x \) to one side

Next, we want to move all terms involving \( x \) to one side of the equation and constant terms to the other side. We can do this by subtracting \( 12x \) from both sides:

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

This simplifies to:

\[ -10x - 5 = 15 \]

Step 3: Move the constants to the other side

Now, we can add 5 to both sides to isolate the term with \( x \):

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

This simplifies to:

\[ -10x = 20 \]

Step 4: Solve for \( x \)

Now, we divide both sides by -10 to solve for \( x \):

\[ x = \frac{20}{-10} = -2 \]

Solution

Thus, the solution to the equation \( 2x - 5 = 3(4x + 5) \) is:

\[ \boxed{-2} \]