74=5y-2

Rewrite the equation as 5y-2=74.

5y-2=74

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

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 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