To solve the inequality \( 3(x + 4) \geq 2x + 5 \), follow these steps:
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Distribute the 3 on the left side: \[ 3x + 12 \geq 2x + 5 \]
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Subtract \( 2x \) from both sides to get all the \( x \) terms on one side: \[ 3x - 2x + 12 \geq 5 \] Simplifying this, we have: \[ x + 12 \geq 5 \]
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Subtract 12 from both sides to isolate \( x \): \[ x \geq 5 - 12 \] Simplifying gives: \[ x \geq -7 \]
Thus, the solution to the inequality \( 3(x + 4) \geq 2x + 5 \) is: \[ \boxed{x \geq -7} \]
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