Question

ustify your steps using the properties of equality and determine the number of solutions to the equation 32(4−8x)+5x=1−7x .

Answer 1

To solve the equation 32(4-8x) + 5x = 1 - 7x, we will use the properties of equality and simplify each side step by step.

Step 1: Distribute the 32 to the terms inside the parentheses:
32(4) - 32(8x) + 5x = 1 - 7x

Simplifying this gives us:
128 - 256x + 5x = 1 - 7x

Step 2: Combine like terms on each side of the equation:
(128 - 256x + 5x) = (1 - 7x)

128 - 251x = 1 - 7x

Step 3: Group the x terms on one side of the equation and the constant terms on the other side:
-251x + 7x = 1 - 128

Simplifying this gives us:
-244x = -127

Step 4: Divide both sides of the equation by -244 to isolate x:
-244x / -244 = -127 / -244

Simplifying this gives us:
x = 127 / 244

Therefore, the solution to the equation is x = 127/244.

Since x is a specific value, there is only one solution to the equation.