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Math  /  Algebra

Question94y−12=14y−4\frac{9}{4} y-12=\frac{1}{4} y-4

Studdy Solution

STEP 1

1. The given equation is 94y−12=14y−4\frac{9}{4}y - 12 = \frac{1}{4}y - 4.
2. The goal is to solve for yy.
3. We will use algebraic manipulation to isolate the variable yy.

STEP 2

1. Eliminate the fractions by multiplying through by the least common multiple of the denominators.
2. Move all terms involving yy to one side of the equation.
3. Move all constant terms to the opposite side of the equation.
4. Solve for the variable yy.

STEP 3

Multiply through by 4 (the least common multiple of the denominators) to eliminate the fractions.
4(94y−12)=4(14y−4) 4 \left( \frac{9}{4}y - 12 \right) = 4 \left( \frac{1}{4}y - 4 \right)
This simplifies to:
9y−48=y−16 9y - 48 = y - 16

STEP 4

Move all terms involving yy to one side of the equation by subtracting yy from both sides.
9y−y−48=y−y−16 9y - y - 48 = y - y - 16
This simplifies to:
8y−48=−16 8y - 48 = -16

STEP 5

Move all constant terms to the other side of the equation by adding 48 to both sides.
8y−48+48=−16+48 8y - 48 + 48 = -16 + 48
This simplifies to:
8y=32 8y = 32

STEP 6

Solve for yy by dividing both sides by 8.
y=328 y = \frac{32}{8}
This simplifies to:
y=4 y = 4
Solution: The value of yy is 44.

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