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

Question

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

GPT-4o mini · Answer

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

make it way more short and simple

GPT-4o mini · Answer

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:

\[ \boxed{-2} \]