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Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2?
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Solve the following equations using transportation matter and chapter ...
Given Equation:
\[ (x-2)(x+5) + 12 = (x+3)(x-4) - 2 \]
Solution:
Expand and Simplify:
- Expand both sides of the equation:
\[ (x^2 + 5x - 2x - 10) + 12 = (x^2 - 4x + 3x - 12) - 2 \]
- Simplify:
\[ x^2 + 3x + 2 = x^2 - x - 14 - 2 \]
Combine Like Terms:
- Bring like terms to one side of the equation:
\[ x^2 + 3x + 2 = x^2 - x - 16 \]
\[ 3x + 2 = -x - 16 \]
Isolate Variable x:
- Move all x terms to one side:
\[ 3x + x = -16 - 2 \]
\[ 4x = -18 \]
\[ x = -\frac{18}{4} \]
\[ x = -4.5 \]
Check Solution:
- Substitute x = -4.5 back into the original equation to verify the solution:
\[ (-4.5 - 2)(-4.5 + 5) + 12 = (-4.5 + 3)(-4.5 - 4) - 2 \]
\[ (-6.5)(0.5) + 12 = (-1.5)(-8.5) - 2 \]
\[ -3.25 + 12 = 12.75 - 2 \]
\[ 8.75 = 10.75 \]
- Since the last equation is false, the solution x = -4.5 is incorrect.
Conclusion:
- The given equation has no solution.
\[ (x-2)(x+5) + 12 = (x+3)(x-4) - 2 \]
Solution:
Expand and Simplify:
- Expand both sides of the equation:
\[ (x^2 + 5x - 2x - 10) + 12 = (x^2 - 4x + 3x - 12) - 2 \]
- Simplify:
\[ x^2 + 3x + 2 = x^2 - x - 14 - 2 \]
Combine Like Terms:
- Bring like terms to one side of the equation:
\[ x^2 + 3x + 2 = x^2 - x - 16 \]
\[ 3x + 2 = -x - 16 \]
Isolate Variable x:
- Move all x terms to one side:
\[ 3x + x = -16 - 2 \]
\[ 4x = -18 \]
\[ x = -\frac{18}{4} \]
\[ x = -4.5 \]
Check Solution:
- Substitute x = -4.5 back into the original equation to verify the solution:
\[ (-4.5 - 2)(-4.5 + 5) + 12 = (-4.5 + 3)(-4.5 - 4) - 2 \]
\[ (-6.5)(0.5) + 12 = (-1.5)(-8.5) - 2 \]
\[ -3.25 + 12 = 12.75 - 2 \]
\[ 8.75 = 10.75 \]
- Since the last equation is false, the solution x = -4.5 is incorrect.
Conclusion:
- The given equation has no solution.
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Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2?
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Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2?.
Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following equations using transportation matter and chapter solution the question is a bracket (x- 2 )(x+ 5) +12 = (x+ 3) (x- 4) - 2?.
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