Solve for b 1/b-4=-3/(4b)-2 1/4

Math
1b-4=-34b-214
Simplify -34b-214.
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Convert 214 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
1b-4=-34b-(2+14)
Add 2 and 14.
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To write 2 as a fraction with a common denominator, multiply by 44.
1b-4=-34b-(2⋅44+14)
Combine 2 and 44.
1b-4=-34b-(2⋅44+14)
Combine the numerators over the common denominator.
1b-4=-34b-2⋅4+14
Simplify the numerator.
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Multiply 2 by 4.
1b-4=-34b-8+14
Add 8 and 1.
1b-4=-34b-94
1b-4=-34b-94
1b-4=-34b-94
1b-4=-34b-94
Move the negative in front of the fraction.
1b-4=-34b-94
1b-4=-34b-94
Move all terms not containing b to the right side of the equation.
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Add 4 to both sides of the equation.
1b=-34b-94+4
To write 4 as a fraction with a common denominator, multiply by 44.
1b=-34b-94+4⋅44
Combine 4 and 44.
1b=-34b-94+4⋅44
Combine the numerators over the common denominator.
1b=-34b+-9+4⋅44
Simplify the numerator.
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Multiply 4 by 4.
1b=-34b+-9+164
Add -9 and 16.
1b=-34b+74
1b=-34b+74
1b=-34b+74
Find the LCD of the terms in the equation.
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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
b,4b,4
Since b,4b,4 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,4,4 then find LCM for the variable part b1,b1.
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
4 has factors of 2 and 2.
2⋅2
Multiply 2 by 2.
4
The factor for b1 is b itself.
b1=b
b occurs 1 time.
The LCM of b1,b1 is the result of multiplying all prime factors the greatest number of times they occur in either term.
b
The LCM for b,4b,4 is the numeric part 4 multiplied by the variable part.
4b
4b
Multiply each term by 4b and simplify.
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Multiply each term in 1b=-34b+74 by 4b in order to remove all the denominators from the equation.
1b⋅(4b)=-34b⋅(4b)+74⋅(4b)
Simplify 1b⋅(4b).
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Rewrite using the commutative property of multiplication.
41bb=-34b⋅(4b)+74⋅(4b)
Combine 4 and 1b.
4bb=-34b⋅(4b)+74⋅(4b)
Cancel the common factor of b.
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Cancel the common factor.
4bb=-34b⋅(4b)+74⋅(4b)
Rewrite the expression.
4=-34b⋅(4b)+74⋅(4b)
4=-34b⋅(4b)+74⋅(4b)
4=-34b⋅(4b)+74⋅(4b)
Simplify each term.
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Cancel the common factor of 4b.
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Move the leading negative in -34b into the numerator.
4=-34b⋅(4b)+74⋅(4b)
Cancel the common factor.
4=-34b⋅(4b)+74⋅(4b)
Rewrite the expression.
4=-3+74⋅(4b)
4=-3+74⋅(4b)
Cancel the common factor of 4.
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Factor 4 out of 4b.
4=-3+74⋅(4(b))
Cancel the common factor.
4=-3+74⋅(4b)
Rewrite the expression.
4=-3+7⋅b
4=-3+7b
4=-3+7b
4=-3+7b
Solve the equation.
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Rewrite the equation as -3+7b=4.
-3+7b=4
Move all terms not containing b to the right side of the equation.
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Add 3 to both sides of the equation.
7b=4+3
Add 4 and 3.
7b=7
7b=7
Divide each term by 7 and simplify.
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Divide each term in 7b=7 by 7.
7b7=77
Cancel the common factor of 7.
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Cancel the common factor.
7b7=77
Divide b by 1.
b=77
b=77
Divide 7 by 7.
b=1
b=1
b=1
Exclude the solutions that do not make 1b-4=-34b-214 true.
No solution
Solve for b 1/b-4=-3/(4b)-2 1/4

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