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:

(addition/subtraction property of equalities)

step 3. move constant to the other side of equation:

( addition/subtraction property of equalities)

step. isolate your variable:

(multiplication/ division property of equalities)

Answer 1

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

### Step 1: Distributive Property
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, the equation becomes:
\[
2x - 5 = 12x + 15
\]

### Step 2: Move variables to one side of the equation
To move the variable terms to one side, we will subtract \(12x\) from both sides of the equation using the addition/subtraction property of equalities.

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

Combining like terms:
\[
-10x - 5 = 15
\]

### Step 3: Move constant to the other side of the equation
Next, we need to get the constants by themselves on one side. We can add \(5\) to both sides:

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

This simplifies to:
\[
-10x = 20
\]

### Step 4: Isolate your variable
Finally, we will isolate \(x\) by dividing both sides of the equation by \(-10\) using the multiplication/division property of equalities.

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

This further simplifies to:
\[
x = -2
\]

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

\[
\boxed{-2}
\]