Questions: Solve the equation for (x). [ 4(3 x+7)=12 x+28 ]

Solve the equation for (x). [ 4(3 x+7)=12 x+28 ]
Transcript text: Solve the equation for $x$. \[ 4(3 x+7)=12 x+28 \]
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Solution

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Solution Steps

Step 1: Distribute the 4 on the left side

First, distribute the 4 across the terms inside the parentheses on the left side of the equation:

\[ 4(3x + 7) = 12x + 28 \]

This becomes:

\[ 12x + 28 = 12x + 28 \]

Step 2: Simplify the equation

Subtract \(12x\) from both sides of the equation to simplify:

\[ 12x + 28 - 12x = 12x + 28 - 12x \]

This simplifies to:

\[ 28 = 28 \]

Step 3: Analyze the result

The equation \(28 = 28\) is always true, indicating that the original equation is an identity. This means that any value of \(x\) will satisfy the equation.

Final Answer

\[ \boxed{\text{The equation is an identity; any value of } x \text{ is a solution.}} \]

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