Solve the following equation:

• 3x + 2(x + 2) = 20(2x - 5).

To solve the equation \(3x + 2(x + 2) = 20(2x - 5)\), we will first simplify both sides step by step.

Step 1: Distribute the Terms

Start by distributing the \(2\) on the left side and the \(20\) on the right side:

• Left side: \(3x + 2x + 4\)
• Right side: \(40x - 100\)

Step 2: Combine Like Terms

Now, combine the like terms on the left side:

Left side becomes \(5x + 4\).

Step 3: Set Up the Equation

Your equation now looks like this:

5x + 4 = 40x - 100

Step 4: Move Variables to One Side

Next, let's get all the \(x\) terms on one side by subtracting \(5x\) from both sides:

4 = 35x - 100

Step 5: Isolate the Variable

Add \(100\) to both sides to isolate the term with \(x\):

104 = 35x

Step 6: Solve for x

Finally, divide both sides by \(35\):

x = \frac{104}{35}

Final Answer

Thus, the solution to the equation is:

x = 2.9714 (approximately).