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)

Question

Steps:
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 4: Isolate your variable:
(Multiplication/Division Property of Equalities)

Answer 1

Let's solve the equation \(2x - 5 = 3(4x + 5)\) by following the steps you provided.

Step 1: Distributive Property

First, we apply the distributive property on the right-hand side of the equation: \[ 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \] So the equation becomes: \[ 2x - 5 = 12x + 15 \]

Step 2: Move variables to one side of the equation

Next, we want to move all the variable terms to one side of the equation. We’ll subtract \(12x\) from both sides: \[ 2x - 12x - 5 = 12x - 12x + 15 \] This simplifies to: \[ -10x - 5 = 15 \]

Step 3: Move constant to the other side of the equation

Now, we add \(5\) to both sides to isolate the variable term: \[ -10x - 5 + 5 = 15 + 5 \] This simplifies to: \[ -10x = 20 \]

Step 4: Isolate your variable

Finally, we want to isolate \(x\). We do this by dividing both sides by \(-10\): \[ \frac{-10x}{-10} = \frac{20}{-10} \] This simplifies to: \[ x = -2 \]

Thus, the solution to the equation \(2x - 5 = 3(4x + 5)\) is: \[ \boxed{-2} \]