Question
Solve for \( y \). \( -3 y+6(9 y+4)=6-4(9-y) \) \( y= \)
Ask by Ward Reid. in the United States
Mar 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y = -\frac{54}{47} \)
Solution
Solve the equation \( -3y+6(9y+4)=6-4(9-y) \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(-3y+6\left(9y+4\right)=6-4\left(9-y\right)\)
- step1: Move the expression to the left side:
\(-3y+6\left(9y+4\right)-\left(6-4\left(9-y\right)\right)=0\)
- step2: Remove the parentheses:
\(-3y+6\left(9y+4\right)-6+4\left(9-y\right)=0\)
- step3: Calculate:
\(47y+54=0\)
- step4: Move the constant to the right side:
\(47y=0-54\)
- step5: Remove 0:
\(47y=-54\)
- step6: Divide both sides:
\(\frac{47y}{47}=\frac{-54}{47}\)
- step7: Divide the numbers:
\(y=-\frac{54}{47}\)
The solution to the equation \( -3y+6(9y+4)=6-4(9-y) \) is \( y = -\frac{54}{47} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
First, let's simplify the equation step-by-step. Starting with: \[ -3y + 6(9y + 4) = 6 - 4(9 - y) \] Distribute the 6 and -4: \[ -3y + 54y + 24 = 6 - 36 + 4y \] Combine like terms on both sides: \[ (54y - 3y) + 24 = (4y - 30) \] \[ 51y + 24 = 4y - 30 \] Now, isolate \( y \). Subtract \( 4y \) from both sides: \[ 51y - 4y + 24 = -30 \] \[ 47y + 24 = -30 \] Next, subtract 24 from both sides: \[ 47y = -30 - 24 \] \[ 47y = -54 \] Finally, divide by 47: \[ y = \frac{-54}{47} \] So the solution is: \[ y = -\frac{54}{47} \]
