7y-11=9y-15

To remove the radical on the left side of the equation, square both sides of the equation.

7y-112=9y-152

Multiply the exponents in ((7y-11)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(7y-11)12⋅2=9y-152

Cancel the common factor of 2.

Cancel the common factor.

(7y-11)12⋅2=9y-152

Rewrite the expression.

(7y-11)1=9y-152

(7y-11)1=9y-152

(7y-11)1=9y-152

Simplify.

7y-11=9y-152

Factor 3 out of 9y-15.

Factor 3 out of 9y.

7y-11=3(3y)-152

Factor 3 out of -15.

7y-11=3(3y)+3(-5)2

Factor 3 out of 3(3y)+3(-5).

7y-11=3(3y-5)2

7y-11=3(3y-5)2

Rewrite 3(3y-5)2 as 3(3y-5).

Use axn=axn to rewrite 3(3y-5) as (3(3y-5))12.

7y-11=((3(3y-5))12)2

Apply the power rule and multiply exponents, (am)n=amn.

7y-11=(3(3y-5))12⋅2

Combine 12 and 2.

7y-11=(3(3y-5))22

Cancel the common factor of 2.

Cancel the common factor.

7y-11=(3(3y-5))22

Divide 1 by 1.

7y-11=(3(3y-5))1

7y-11=(3(3y-5))1

Simplify.

7y-11=3(3y-5)

7y-11=3(3y-5)

Apply the distributive property.

7y-11=3(3y)+3⋅-5

Multiply 3 by 3.

7y-11=9y+3⋅-5

Multiply 3 by -5.

7y-11=9y-15

7y-11=9y-15

Move all terms containing y to the left side of the equation.

Subtract 9y from both sides of the equation.

7y-11-9y=-15

Subtract 9y from 7y.

-2y-11=-15

-2y-11=-15

Move all terms not containing y to the right side of the equation.

Add 11 to both sides of the equation.

-2y=-15+11

Add -15 and 11.

-2y=-4

-2y=-4

Divide each term by -2 and simplify.

Divide each term in -2y=-4 by -2.

-2y-2=-4-2

Cancel the common factor of -2.

Cancel the common factor.

-2y-2=-4-2

Divide y by 1.

y=-4-2

y=-4-2

Divide -4 by -2.

y=2

y=2

y=2

Solve for y square root of 7y-11 = square root of 9y-15