To determine how many solutions the equation \( 3(x + 1) + 2 = 5x \) has, we first need to simplify it.
-
Distribute \( 3 \) in the left-hand side: \[ 3(x + 1) = 3x + 3 \] Thus, the equation becomes: \[ 3x + 3 + 2 = 5x \]
-
Combine like terms: \[ 3x + 5 = 5x \]
-
Next, rearrange the equation to solve for \( x \): \[ 5 = 5x - 3x \] This simplifies to: \[ 5 = 2x \]
-
Divide both sides by \( 2 \): \[ x = \frac{5}{2} \]
Now, we have found a single solution, \( x = \frac{5}{2} \).
Thus, the equation \( 3(x + 1) + 2 = 5x \) has one solution.