Solving Equations with Fractions

How do I solve this?
1/3(7y-1)+1/6(4y+7)

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Karin from Algebra Class says:

I would love to help you solve this equation, however, we need to have an equal sign with an answer:

1/3(7y-1) + 1/6(4y + 7) = ???

If the directions are to simplify, then we can:

Step 1: Get rid of the fractions by multiplying all terms by 6.

61/3(7y-1) + 1/6(4y +7)
2(7y-1) +1(4y+7)

Step 2: Use the distributive property:
2(7y-1) +1(4y+7)
14y -2 + 4y + 7

Step 3: Write like terms together:
14y -2 + 4y + 7
14y + 4y - 2 + 7

Step 4: Combine like terms:
14y + 4y - 2 + 7
18y + 5

Step 5: Since we are simplifying an expression (and not solving an equation where we would keep the equation balanced by multiplying by 6 on both sides), we need to divide our answer by 6.

We multiplied by 6 initially to get rid of the fractions and now we must divide our answer by 6 in order to keep it balanced.

18y/6 + 5/6

Simplifies to 3y + 5/6

Hope this helps,
Karin

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