Question:

Solve the inequality: \[ 6(x - 1)<7(3 - x) \]

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When solving inequalities, carefully rearrange and watch the direction of inequality signs. Dividing by positive numbers does not flip the sign.
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.
\[ 6(x - 1)<7(3 - x) \] \[ 6x - 6<21 - 7x \]
Step 2: Collect like terms.
\[ 6x + 7x<21 + 6 \] \[ 13x<27 \]
Step 3: Solve for \(x\).
\[ x<\frac{27}{13} \approx 2.07 \]
Step 4: Match with given options.
Among the answer choices, only the option \(x>-1117\) is always true given the inequality holds for all \(x<2.07\).
Final Answer: \[ \boxed{x>-1117} \]
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