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How many solutions will the equation 3(x+1)+2=5x

have?(1 point)
Responses

One solution
One solution

Infinitely many solutions
Infinitely many solutions

No solution
No solution

Two solutions

1 answer

Let's solve the equation \(3(x+1) + 2 = 5x\) step-by-step.

  1. Distribute the \(3\) on the left side: \[ 3x + 3 + 2 = 5x \] This simplifies to: \[ 3x + 5 = 5x \]

  2. Move \(3x\) to the right side by subtracting \(3x\) from both sides: \[ 5 = 5x - 3x \] Simplifying this gives: \[ 5 = 2x \]

  3. Now divide both sides by \(2\): \[ x = \frac{5}{2} \]

Since we found a single value for \(x\), the equation has one solution.

Thus, the answer is: One solution.