Use the following steps 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

To solve the equation $2x-5=3(4x+5)$ using the specified steps, let's go through each step in detail.

Step 1: Distributive Property

We need to apply the distributive property to the right side of the equation:

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

Now, substitute this back into the equation:

$$2x-5=12x+15$$

Step 2: Move variables to one side of the equation

Next, we will move the variable terms so that all terms involving $x$ are on one side of the equation. Subtract $12x$ from both sides:

$$2x-12x-5=15$$ This simplifies to:

$$-10x-5=15$$

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

Now, we will move the constant term to the other side by adding $5$ to both sides:

$$-10x-5+5=15+5$$ This simplifies to:

$$-10x=20$$

Step 4: Isolate your variable

To isolate $x$, we will divide both sides by $-10$:

$$x=\frac{20}{-10}$$ This simplifies to:

$$x=-2$$

Final Answer

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

$$\boxed{{\displaystyle -2}}$$