Questions: What is the error in this linear equation? 5(1+4 y)+2 y=-27 5+20 y+2 y=-27 27 y/27=27/27 y=1

What is the error in this linear equation? 5(1+4 y)+2 y=-27 5+20 y+2 y=-27 27 y/27=27/27 y=1
Transcript text: What is the error in this linear equation? \[ \begin{array}{c} 5(1+4 y)+2 y=-27 \\ 5+20 y+2 y=-27 \\ \frac{27 y}{27}=\frac{27}{27} \\ y=1 \end{array} \]
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Solution

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Solution Steps

To identify the error in the given linear equation, we need to carefully follow each step of the solution and check for any mistakes in the algebraic manipulations.

  1. Distribute the 5 in the first equation.
  2. Combine like terms.
  3. Solve for \( y \).
Step 1: Distribute the 5 in the first equation

Starting with the equation: \[ 5(1 + 4y) + 2y = -27 \] Distribute the 5: \[ 5 \cdot 1 + 5 \cdot 4y + 2y = -27 \] This simplifies to: \[ 5 + 20y + 2y = -27 \]

Step 2: Combine like terms

Combine the \( y \) terms: \[ 5 + 22y = -27 \]

Step 3: Isolate the variable \( y \)

Subtract 5 from both sides: \[ 22y = -27 - 5 \] \[ 22y = -32 \] Divide both sides by 22: \[ y = \frac{-32}{22} \] Simplify the fraction: \[ y = -\frac{16}{11} \]

Final Answer

\(\boxed{y = -\frac{16}{11}}\)

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