Solve 3(5x - 7) - 2(9x - 11) = 4(8x - 13) - 17

To solve the equation 3(5x - 7) - 2(9x - 11) = 4(8x - 13) - 17, we will first simplify both sides step by step.

Step 1: Distribute the Terms

Start by distributing the numbers outside the parentheses:

• Left side: 3 * 5x - 3 * 7 - 2 * 9x + 2 * 11
• Right side: 4 * 8x - 4 * 13 - 17

This gives us:

• Left side: 15x - 21 - 18x + 22
• Right side: 32x - 52 - 17

Step 2: Combine Like Terms

Now, combine the like terms on both sides:

• Left side: (15x - 18x) + (-21 + 22) = -3x + 1
• Right side: 32x - 69

Step 3: Set the Equation

Now we have:

-3x + 1 = 32x - 69

Step 4: Isolate x

Next, we will isolate x by moving all terms involving x to one side and constant terms to the other:

• Add 3x to both sides:
• 1 = 35x - 69

Then, add 69 to both sides:

70 = 35x

Step 5: Solve for x

Finally, divide both sides by 35:

x = 70 / 35

This simplifies to:

x = 2

Final Answer

The solution to the equation is x = 2.