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Math  /  Algebra

Question2y−5=y+42 y-5=y+4

Studdy Solution

STEP 1

1. The equation 2y−5=y+4 2y - 5 = y + 4 is a linear equation in one variable.
2. The goal is to solve for the variable y y .
3. The equation involves basic algebraic operations like addition and subtraction.

STEP 2

1. Simplify the equation by moving all terms involving y y to one side.
2. Isolate the variable y y by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

To simplify the equation, we need to get all the terms involving y y on one side. Subtract y y from both sides:
2y−5−y=y+4−y 2y - 5 - y = y + 4 - y
This simplifies to:
y−5=4 y - 5 = 4

STEP 4

Now, isolate y y by adding 5 to both sides of the equation:
y−5+5=4+5 y - 5 + 5 = 4 + 5
This simplifies to:
y=9 y = 9

STEP 5

Check the solution by substituting y=9 y = 9 back into the original equation:
2(9)−5=9+4 2(9) - 5 = 9 + 4
Simplify both sides:
18−5=13 18 - 5 = 13
9+4=13 9 + 4 = 13
Both sides are equal, confirming our solution is correct.
The solution is:
9 \boxed{9}

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