Questions: Consider the following equation: 3y-4-9=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: \[ 3|y-4|-9=0 \] Step 1 of 4 : Rewrite the equation above in standard form and determine if there is a solution.

Solution

Solution Steps

Step 1: Rewrite the equation in standard form

The given equation is: \[ 3|y - 4| - 9 = 0 \]

First, isolate the absolute value term: \[ 3|y - 4| = 9 \]

Next, divide both sides by 3: \[ |y - 4| = 3 \]

Step 2: Determine the solutions for the absolute value equation

The absolute value equation \( |y - 4| = 3 \) can be split into two separate equations: \[ y - 4 = 3 \] \[ y - 4 = -3 \]

Step 3: Solve each equation

Solve the first equation: \[ y - 4 = 3 \] \[ y = 7 \]

Solve the second equation: \[ y - 4 = -3 \] \[ y = 1 \]

Final Answer

The solutions to the equation are: \[ y = 7 \] \[ y = 1 \]

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