Let's solve the equation step by step:
We start with the equation: \[ 13x + 2x + 10 = -2 + 3(5x + 4) \]
First, combine like terms on the left side: \[ 15x + 10 = -2 + 3(5x + 4) \]
Now, let's simplify the right side. Start by distributing the 3: \[ 3(5x + 4) = 15x + 12 \] So, the equation now is: \[ 15x + 10 = -2 + 15x + 12 \]
Next, simplify the right side by combining like terms: \[ -2 + 12 = 10 \] Thus, the equation simplifies to: \[ 15x + 10 = 15x + 10 \]
This equation is true for all values of \( x \). This means that there are infinitely many solutions because every value of \( x \) satisfies the equation.
Final answer: Infinitely many solutions.
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