Solve for y. 9/4y – 12 = 1/4y – 4
The correct answer and explanation is:
We are given the equation: 94y−12=14y−4\frac{9}{4}y – 12 = \frac{1}{4}y – 4
Step 1: Eliminate fractions
To make it easier, multiply every term in the equation by 4 to eliminate the denominators: 4(94y−12)=4(14y−4)4 \left( \frac{9}{4}y – 12 \right) = 4 \left( \frac{1}{4}y – 4 \right) 9y−48=y−169y – 48 = y – 16
Step 2: Move all terms involving y to one side
Subtract y from both sides: 9y−y−48=y−y−169y – y – 48 = y – y – 16 8y−48=−168y – 48 = -16
Step 3: Isolate the variable
Add 48 to both sides: 8y=328y = 32
Step 4: Solve for y
Divide both sides by 8: y=328=4y = \frac{32}{8} = 4
✅ Final Answer:
y=4\boxed{y = 4}
300-Word Explanation:
This problem is a linear equation that contains fractions, and solving it involves basic algebraic steps: eliminating fractions, combining like terms, and isolating the variable.
First, we notice that the equation has fractional coefficients: 94y\frac{9}{4}y and 14y\frac{1}{4}y. Dealing with fractions directly can be messy, so we simplify by multiplying the entire equation by 4, the least common denominator (LCD). This step eliminates all denominators, turning the equation into standard form with integers.
After clearing fractions, the equation becomes: 9y−48=y−169y – 48 = y – 16
Next, we isolate the variable yy by moving all terms containing yy to one side and constant terms to the other. Subtracting yy from both sides simplifies the equation to: 8y−48=−168y – 48 = -16
We then move the constant by adding 48 to both sides: 8y=328y = 32
Finally, dividing both sides by 8 gives us the solution: y=4y = 4
We can check our solution by plugging y=4y = 4 back into the original equation: 94(4)−12=14(4)−4⇒9−12=1−4⇒−3=−3\frac{9}{4}(4) – 12 = \frac{1}{4}(4) – 4 \Rightarrow 9 – 12 = 1 – 4 \Rightarrow -3 = -3
Since both sides are equal, the solution is correct.