Question

Help please ! solve for y and simplify the answer

Answer 1

y = 11.5

Explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

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First, cross-multiply. Multiply 5 and y - 4 to both sides of the equation:

`(y - 4) * (5) * (6)/(5) = (9)/(y - 4) * (y - 4) * (5)`

`6(y - 4) = 9 * 5\\6(y - 4) = 45`

Next, isolate the variable, y. First, divide 6 from both sides of the equation:

`(6(y - 4))/(6) = (45)/(6) \\y - 4 = (45)/(6) \\y - 4 = 7.5\\`

Then, add 4 to both sides of the equation:

`y - 4 = 7.5\\y - 4 (+4) = 7.5 (+4)\\y = 7.5 + 4\\y = 11.5`

y = 11.5 is your answer.

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Answer 2

y = 11.5

Explanation:

`(6)/(5) = (9)/(y-4)`

We are solving for y. Currently, y is in the denominator. We want it in the numerator so we will multiply the whole binomial (y - 4) to both sides.

`((y-4)/(1) )(6)/(5) = (9)/(y-4)((y -4)/(1))`

On the right side, (y - 4) cancels out leaving us with 9.

On the left side, we want to distribute the 6 in the numerator across the parentheses. Also multiply the denominators together.

`((6y - 24)/(5)) = 9`

Now we want to continue to isolate y.

Multiply both sides by 5 to get rid of the denominator.

`6y - 24 = 45`

Add 24 to both sides.

`6y = 69`

Divide both sides by 6.

`y = 11.5`

This is your answer.

Let's check it by plugging y = 11.5 back into the original equation.

`(6)/(5) = (9)/(11.5-4)`

Simplify.

`(6)/(5) = (9)/(7.5)`

Divide.

`1.2 = 1.2`

Your answer is correct.

Hope this helps!