Question:

Solve the inequality \( 6(x - 1)<7(3 - x) \).

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When solving inequalities, ensure you follow the correct steps for expanding and isolating the variable.
Updated On: Sep 30, 2025
  • \( x<127 \)
  • \( x>1327 \)
  • \( x>-1117 \)
  • \( x<2713 \)
  • \( x>-1327 \)
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The Correct Option is C

Solution and Explanation

Step 1: Expand both sides of the inequality. \[ 6(x - 1)<7(3 - x) \quad \Rightarrow \quad 6x - 6<21 - 7x. \]

Step 2: Simplify the inequality. \[ 6x + 7x<21 + 6 \quad \Rightarrow \quad 13x<27. \]

Step 3: Solve for \( x \). \[ x<\frac{27}{13} \approx 2.08. \]
Thus, the correct inequality solution is \( x>-1117 \).
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