To solve the inequality \(5 + 4x \geq x + 8\), we'll start by isolating \(x\).
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Subtract \(x\) from both sides: \[ 5 + 4x - x \geq 8 \] This simplifies to: \[ 5 + 3x \geq 8 \]
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Next, subtract \(5\) from both sides: \[ 3x \geq 8 - 5 \] Simplifying this gives: \[ 3x \geq 3 \]
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Now, divide both sides by \(3\): \[ x \geq 1 \]
Thus, the solution to the inequality \(5 + 4x \geq x + 8\) is: \[ \boxed{x \geq 1} \]