To solve the equation \( 5x - 2 + x = 9 + 3x + 10 \), let's first simplify both sides.
Combine like terms on both sides:
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On the left side: \[ 5x + x - 2 = 6x - 2 \]
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On the right side: \[ 9 + 10 + 3x = 19 + 3x \]
Now the equation looks like this: \[ 6x - 2 = 19 + 3x \]
Next, we will isolate \( x \) by moving all \( x \) terms to one side and constant terms to the other side. First, subtract \( 3x \) from both sides: \[ 6x - 3x - 2 = 19 \] This simplifies to: \[ 3x - 2 = 19 \]
Now, add \( 2 \) to both sides: \[ 3x = 19 + 2 \] Simplifying this gives: \[ 3x = 21 \]
Finally, divide both sides by \( 3 \): \[ x = \frac{21}{3} = 7 \]
So the solution is: \[ \boxed{7} \]