Questions: Consider the following equation: 2 y+7-7=0 Step 1 of 4: Rewrite the equation above in standard form and determine if there is a solution.

Consider the following equation: 2 y+7-7=0 Step 1 of 4: Rewrite the equation above in standard form and determine if there is a solution.
Transcript text: Consider the following equation: \[ |2 y+7|-7=0 \] Step 1 of 4: Rewrite the equation above in standard form and determine if there is a solution.
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Solution

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Solution Steps

Step 1: Rewrite the Equation in Standard Form

The given equation is:

\[ |2y + 7| - 7 = 0 \]

Add 7 to both sides to rewrite it in standard form:

\[ |2y + 7| = 7 \]

Step 2: Solve the Absolute Value Equation

The absolute value equation \( |2y + 7| = 7 \) can be split into two separate linear equations:

  1. \( 2y + 7 = 7 \)
  2. \( 2y + 7 = -7 \)
Step 3: Solve Each Linear Equation

Equation 1:

\[ 2y + 7 = 7 \]

Subtract 7 from both sides:

\[ 2y = 0 \]

Divide by 2:

\[ y = 0 \]

Equation 2:

\[ 2y + 7 = -7 \]

Subtract 7 from both sides:

\[ 2y = -14 \]

Divide by 2:

\[ y = -7 \]

Final Answer

The solutions to the equation are:

\[ \boxed{y = 0} \quad \text{and} \quad \boxed{y = -7} \]

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