# Solve for y v((3y)/4-1)=5y-3

v(3y4-1)=5y-3
Simplify v(3y4-1).
Simplify terms.
Apply the distributive property.
v3y4+v⋅-1=5y-3
Combine v and 3y4.
v(3y)4+v⋅-1=5y-3
Move -1 to the left of v.
v(3y)4-1⋅v=5y-3
v(3y)4-1⋅v=5y-3
Simplify each term.
Move 3 to the left of v.
3⋅vy4-1⋅v=5y-3
Rewrite -1v as -v.
3vy4-v=5y-3
3vy4-v=5y-3
3vy4-v=5y-3
Subtract 5y from both sides of the equation.
3vy4-v-5y=-3
Add v to both sides of the equation.
3vy4-5y=-3+v
Factor y out of 3vy4-5y.
Factor y out of 3vy4.
y(3v4)-5y=-3+v
Factor y out of -5y.
y(3v4)+y⋅-5=-3+v
Factor y out of y3v4+y⋅-5.
y(3v4-5)=-3+v
y(3v4-5)=-3+v
Divide each term by 3v4-5 and simplify.
Divide each term in y(3v4-5)=-3+v by 3v4-5.
y(3v4-5)3v4-5=-33v4-5+v3v4-5
Cancel the common factor of 3v4-5.
Cancel the common factor.
y(3v4-5)3v4-5=-33v4-5+v3v4-5
Divide y by 1.
y=-33v4-5+v3v4-5
y=-33v4-5+v3v4-5
Simplify -33v4-5+v3v4-5.
Simplify each term.
Simplify the denominator.
To write -5 as a fraction with a common denominator, multiply by 44.
y=-33v4-5⋅44+v3v4-5
Combine -5 and 44.
y=-33v4+-5⋅44+v3v4-5
Combine the numerators over the common denominator.
y=-33v-5⋅44+v3v4-5
Multiply -5 by 4.
y=-33v-204+v3v4-5
y=-33v-204+v3v4-5
Multiply the numerator by the reciprocal of the denominator.
y=-343v-20+v3v4-5
Multiply -343v-20.
Combine -3 and 43v-20.
y=-3⋅43v-20+v3v4-5
Multiply -3 by 4.
y=-123v-20+v3v4-5
y=-123v-20+v3v4-5
Move the negative in front of the fraction.
y=-123v-20+v3v4-5
Simplify the denominator.
To write -5 as a fraction with a common denominator, multiply by 44.
y=-123v-20+v3v4-5⋅44
Combine -5 and 44.
y=-123v-20+v3v4+-5⋅44
Combine the numerators over the common denominator.
y=-123v-20+v3v-5⋅44
Multiply -5 by 4.
y=-123v-20+v3v-204
y=-123v-20+v3v-204
Multiply the numerator by the reciprocal of the denominator.
y=-123v-20+v43v-20
Combine v and 43v-20.
y=-123v-20+v⋅43v-20
Move 4 to the left of v.
y=-123v-20+4v3v-20
y=-123v-20+4v3v-20
Simplify terms.
Combine the numerators over the common denominator.
y=-12+4v3v-20
Factor 4 out of -12+4v.
Factor 4 out of -12.
y=4⋅-3+4v3v-20
Factor 4 out of 4⋅-3+4v.
y=4(-3+v)3v-20
y=4(-3+v)3v-20
Rewrite -3 as -1(3).
y=4(-1(3)+v)3v-20
Factor -1 out of v.
y=4(-1(3)-1(-v))3v-20
Factor -1 out of -1(3)-1(-v).
y=4(-1(3-v))3v-20
Move the negative in front of the fraction.
y=-4(3-v)3v-20
y=-4(3-v)3v-20
y=-4(3-v)3v-20
y=-4(3-v)3v-20
Solve for y v((3y)/4-1)=5y-3

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