Justify your steps using the properties of equality and determine the number of solutions to the equation 3/2(4−8x)+5x=1−7x in two sentences

To solve the equation \(\frac{3}{2}(4 - 8x) + 5x = 1 - 7x\), first distribute \(\frac{3}{2}\) to both terms inside the parentheses, yielding \(6 - 12x + 5x = 1 - 7x\), and then combine like terms and isolate \(x\) by adding \(12x\) and subtracting \(1\) from both sides, resulting in \(6 + 2x = -6\), ultimately giving \(x = -6\). Thus, there is exactly one solution to the equation.