Justify your steps using the properties of equality and determine the number of solutions to the equation 32(4−8x)+5x=1−7x.
To solve the equation 32(4−8x) + 5x = 1−7x, we can follow these steps:
Step 1: Distribute the 32 to the terms inside the parentheses:
32*4 - 32*8x + 5x = 1 - 7x
Step 2: Simplify by performing the multiplications:
128 - 256x + 5x = 1 - 7x
Step 3: Combine like terms by adding and subtracting:
-251x + 5x + 7x = 1 - 128
Step 4: Simplify and combine like terms:
-239x = -127
Step 5: To solve for x, we need to isolate x. Divide both sides of the equation by -239:
x = -127 / -239
Step 6: Simplify the fraction:
x = 127/239
So the solution to the equation is x = 127/239.
There is only one solution to the equation.