Questions: How many solutions exist for the given equation? 3(x+10)+6=3(x+12) zero one two infinitely many

How many solutions exist for the given equation? 3(x+10)+6=3(x+12) zero one two infinitely many
Transcript text: How many solutions exist for the given equation? \[ 3(x+10)+6=3(x+12) \] zero one two infinitely many
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Solution

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Solution Steps

Step 1: Simplify Both Sides of the Equation

Start by expanding both sides of the equation:

\[ 3(x+10) + 6 = 3(x+12) \]

Expanding both sides gives:

\[ 3x + 30 + 6 = 3x + 36 \]

Simplify further:

\[ 3x + 36 = 3x + 36 \]

Step 2: Analyze the Simplified Equation

Notice that both sides of the equation are identical:

\[ 3x + 36 = 3x + 36 \]

This indicates that the equation is true for all values of \(x\).

Final Answer

Since the equation is true for all values of \(x\), there are infinitely many solutions.

\[ \boxed{\text{infinitely many}} \]

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