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For what value of N would the following equation have no solution?
3(4x−7)+12=2(5x−3)+N(x−3)
- a)N=1
- b)N=2
- c)N=-1
- d)N=-2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For what value ofNwould the following equation have no solution?3(4x&m...
Simplify both sides of the equation as much as possible, and solve for x in the equation in terms of N:
3(4x−7)+12=2(5x−3)+N(x−3)
3⋅4x−3⋅7+12=2⋅5x−2⋅3+N⋅x−N⋅3
12x−21+12=10x−6+Nx−3N
12x−9=(10+N)x+(−6−3N)
12x−(10+N)x=(−6−3N)+9
(2−N)x=3−3N
3⋅4x−3⋅7+12=2⋅5x−2⋅3+N⋅x−N⋅3
12x−21+12=10x−6+Nx−3N
12x−9=(10+N)x+(−6−3N)
12x−(10+N)x=(−6−3N)+9
(2−N)x=3−3N
x has exactly one solution unless the denominator is 0 - that is, N=2. We make sure that this value renders no solution by substituting:
3(4x−7)+12=2(5x−3)+N(x−3)
3(4x−7)+12=2(5x−3)+2(x−3)
12x−21+12=10x−6+2x−6
12x−9=12x−12
−9=−12
3(4x−7)+12=2(5x−3)+2(x−3)
12x−21+12=10x−6+2x−6
12x−9=12x−12
−9=−12
The equation has no solution, and N=2 is the correct answer.
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For what value ofNwould the following equation have no solution?3(4x&m...
The equation is incomplete, as it ends with an open parenthesis. Please provide the complete equation so that I can assist you further.
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