Solve for q 11 2/5=q-4 2/7+2 1/7

Math
1125=q-427+217
Convert 1125 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
11+25=q-427+217
Add 11 and 25.
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To write 11 as a fraction with a common denominator, multiply by 55.
11⋅55+25=q-427+217
Combine 11 and 55.
11⋅55+25=q-427+217
Combine the numerators over the common denominator.
11⋅5+25=q-427+217
Simplify the numerator.
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Multiply 11 by 5.
55+25=q-427+217
Add 55 and 2.
575=q-427+217
575=q-427+217
575=q-427+217
575=q-427+217
Simplify q-427+217.
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Convert 427 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
575=q-(4+27)+217
Add 4 and 27.
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To write 4 as a fraction with a common denominator, multiply by 77.
575=q-(4⋅77+27)+217
Combine 4 and 77.
575=q-(4⋅77+27)+217
Combine the numerators over the common denominator.
575=q-4⋅7+27+217
Simplify the numerator.
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Multiply 4 by 7.
575=q-28+27+217
Add 28 and 2.
575=q-307+217
575=q-307+217
575=q-307+217
575=q-307+217
Convert 217 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
575=q-307+2+17
Add 2 and 17.
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To write 2 as a fraction with a common denominator, multiply by 77.
575=q-307+2⋅77+17
Combine 2 and 77.
575=q-307+2⋅77+17
Combine the numerators over the common denominator.
575=q-307+2⋅7+17
Simplify the numerator.
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Multiply 2 by 7.
575=q-307+14+17
Add 14 and 1.
575=q-307+157
575=q-307+157
575=q-307+157
575=q-307+157
Combine fractions with similar denominators.
575=q+-30+157
Simplify the expression.
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Add -30 and 15.
575=q+-157
Move the negative in front of the fraction.
575=q-157
575=q-157
575=q-157
Rewrite the equation as q-157=575.
q-157=575
Move all terms not containing q to the right side of the equation.
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Add 157 to both sides of the equation.
q=575+157
To write 575 as a fraction with a common denominator, multiply by 77.
q=575⋅77+157
To write 157 as a fraction with a common denominator, multiply by 55.
q=575⋅77+157⋅55
Write each expression with a common denominator of 35, by multiplying each by an appropriate factor of 1.
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Multiply 575 and 77.
q=57⋅75⋅7+157⋅55
Multiply 5 by 7.
q=57⋅735+157⋅55
Multiply 157 and 55.
q=57⋅735+15⋅57⋅5
Multiply 7 by 5.
q=57⋅735+15⋅535
q=57⋅735+15⋅535
Combine the numerators over the common denominator.
q=57⋅7+15⋅535
Simplify the numerator.
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Multiply 57 by 7.
q=399+15⋅535
Multiply 15 by 5.
q=399+7535
Add 399 and 75.
q=47435
q=47435
q=47435
The result can be shown in multiple forms.
Exact Form:
q=47435
Decimal Form:
q=13.54285714…
Mixed Number Form:
q=131935
Solve for q 11 2/5=q-4 2/7+2 1/7

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