To solve the inequality \( 5(-2 + x) < 3x + 2 \), we can follow these steps:
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Distribute the 5 on the left side: \[ 5(-2) + 5(x) < 3x + 2 \] This simplifies to: \[ -10 + 5x < 3x + 2 \]
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Next, isolate the terms with \( x \) on one side and the constant terms on the other side. Subtract \( 3x \) from both sides: \[ -10 + 5x - 3x < 2 \] This simplifies to: \[ -10 + 2x < 2 \]
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Now, add 10 to both sides to isolate the term with \( x \): \[ 2x < 2 + 10 \] This simplifies to: \[ 2x < 12 \]
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Divide each side by 2 to solve for \( x \): \[ x < 6 \]
Thus, the solution to the inequality \( 5(-2 + x) < 3x + 2 \) is: \[ x < 6 \]