Let's break down the steps you're following to solve the equation and find the value of \( x \).
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Start with the equation: \[ 60 + 20x = 90 + 10x \]
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To isolate \( x \) on one side, subtract \( 10x \) from both sides: \[ 60 + 20x - 10x = 90 + 10x - 10x \] This simplifies to: \[ 60 + 10x = 90 \]
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Next, subtract 60 from both sides: \[ 60 - 60 + 10x = 90 - 60 \] This simplifies to: \[ 10x = 30 \]
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Finally, divide both sides by 10 to solve for \( x \): \[ x = \frac{30}{10} \] Thus: \[ x = 3 \]
Therefore, the solution for \( x \) is: \[ \boxed{3} \]