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Math  /  Algebra

QuestionSolve for yy. −59=y−3-\frac{5}{9}=y-3
Simplify your answer as much as possible.

Studdy Solution

STEP 1

1. The equation −59=y−3 -\frac{5}{9} = y - 3 is asking us to solve for y y .
2. This is a one-step equation with one solution.
3. The equation involves basic algebraic operations, specifically addition.

STEP 2

1. Isolate the variable y y by performing algebraic operations.
2. Simplify the expression to find the value of y y .
3. Check the solution by substituting it back into the original equation.

STEP 3

To isolate y y , we need to get rid of the −3-3 on the right side of the equation. We do this by adding 33 to both sides of the equation:
−59+3=y−3+3 -\frac{5}{9} + 3 = y - 3 + 3

STEP 4

Simplify the right side of the equation:
−59+3=y -\frac{5}{9} + 3 = y

STEP 5

Now, let's simplify the left side of the equation. Convert 33 to a fraction with a denominator of 99:
3=279 3 = \frac{27}{9}
Now add the fractions:
−59+279=27−59=229 -\frac{5}{9} + \frac{27}{9} = \frac{27 - 5}{9} = \frac{22}{9}
So, y=229 y = \frac{22}{9} .

STEP 6

Check the solution by substituting y=229 y = \frac{22}{9} back into the original equation:
−59=229−3 -\frac{5}{9} = \frac{22}{9} - 3
Convert 33 to a fraction:
229−279=−59 \frac{22}{9} - \frac{27}{9} = -\frac{5}{9}
Both sides are equal, confirming the solution is correct.
The solution is:
229 \boxed{\frac{22}{9}}

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