# Solve for y 7/4=5/y-2 74=5y-2
Rewrite the equation as 5y-2=74.
5y-2=74
Move all terms not containing y to the right side of the equation.
Add 2 to both sides of the equation.
5y=74+2
To write 2 as a fraction with a common denominator, multiply by 44.
5y=74+2⋅44
Combine 2 and 44.
5y=74+2⋅44
Combine the numerators over the common denominator.
5y=7+2⋅44
Simplify the numerator.
Multiply 2 by 4.
5y=7+84
Add 7 and 8.
5y=154
5y=154
5y=154
Set up the rational expression with the same denominator over the entire equation.
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4y. The 5y expression needs to be multiplied by 44 to make the denominator 4y. The 154 expression needs to be multiplied by yy to make the denominator 4y.
5y⋅44=154⋅yy
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4y.
5(4)
Multiply 5 by 4.
204y=154⋅yy
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4y.
15(y)
Multiply 15 by y.
204y=15y4y
204y=15y4y
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
20=15y
Rewrite the equation as 15y=20.
15y=20
Divide each term by 15 and simplify.
Divide each term in 15y=20 by 15.
15y15=2015
Cancel the common factor of 15.
Cancel the common factor.
15y15=2015
Divide y by 1.
y=2015
y=2015
Cancel the common factor of 20 and 15.
Factor 5 out of 20.
y=5(4)15
Cancel the common factors.
Factor 5 out of 15.
y=5⋅45⋅3
Cancel the common factor.
y=5⋅45⋅3
Rewrite the expression.
y=43
y=43
y=43
y=43
The result can be shown in multiple forms.
Exact Form:
y=43
Decimal Form:
y=1.3‾
Mixed Number Form:
y=113
Solve for y 7/4=5/y-2

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