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To solve for x, we need to isolate the variable on one side of the equation.
Starting with the given equation:
5x + 2 = 3x - 20
We want to eliminate the 3x term on the right side of the equation by subtracting 3x from both sides:
5x - 3x + 2 = 3x - 3x - 20
This simplifies to:
2x + 2 = -20
Next, we want to isolate the 2x term on the left side of the equation by subtracting 2 from both sides:
2x + 2 - 2 = -20 - 2
This simplifies to:
2x = -22
Finally, we solve for x by dividing both sides of the equation by 2:
(2x) / 2 = (-22) / 2
This simplifies to:
x = -11
Therefore, the solution to the equation is x = -11.