To solve the equation \( 5(x - 6) + 2 = 7x - 8 \), follow these steps:
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Distribute the \( 5 \) on the left side: \[ 5x - 30 + 2 = 7x - 8 \]
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Combine like terms on the left side: \[ 5x - 28 = 7x - 8 \]
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Get all terms involving \( x \) on one side and constant terms on the other side. Subtract \( 5x \) from both sides: \[ -28 = 7x - 5x - 8 \] \[ -28 = 2x - 8 \]
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Add \( 8 \) to both sides: \[ -28 + 8 = 2x \] \[ -20 = 2x \]
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Divide both sides by \( 2 \): \[ x = -10 \]
So, the solution is \( x = -10 \).
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