Question:
Solve the inequality \(6(x-1)<7(3-x)\).
Solve the inequality \(6(x-1)<7(3-x)\).
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Always expand and isolate variables carefully when solving inequalities. Remember to reverse the sign only when multiplying or dividing by a negative.
Updated On: Oct 3, 2025
- \(x<\tfrac{25}{13}\)
- \(x<2713\)
- \(x<127\)
- \(x>-1327\)
- \(x>-1117\)
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The Correct Option is A
Solution and Explanation
Step 1: Expand both sides.
\[ 6(x-1) = 6x - 6, \quad 7(3-x) = 21 - 7x \] Step 2: Form inequality.
\[ 6x - 6<21 - 7x \] Step 3: Bring variables to one side.
\[ 6x + 7x<21 + 6 \quad \Rightarrow \quad 13x<27 \] Step 4: Solve for \(x\).
\[ x<\tfrac{27}{13} \approx 2.08 \] Final Answer: \[ \boxed{x<\tfrac{27}{13}} \]
\[ 6(x-1) = 6x - 6, \quad 7(3-x) = 21 - 7x \] Step 2: Form inequality.
\[ 6x - 6<21 - 7x \] Step 3: Bring variables to one side.
\[ 6x + 7x<21 + 6 \quad \Rightarrow \quad 13x<27 \] Step 4: Solve for \(x\).
\[ x<\tfrac{27}{13} \approx 2.08 \] Final Answer: \[ \boxed{x<\tfrac{27}{13}} \]
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