justify your steps using the properties of equality and determine the number of solutions to the equation 3/2 (4-8x) + 5x = 1 - 7x

Answer 1

To solve the equation 3/2 (4-8x) + 5x = 1 - 7x, we can follow these steps using the properties of equality:

1. Distribute the 3/2 to the terms inside the parentheses:
(3/2)(4) - (3/2)(8x) + 5x = 1 - 7x

This simplifies to:
6 - 12x/2 + 5x = 1 - 7x

2. Simplify the terms on the left side:
6 - 6x + 5x = 1 - 7x

Combine like terms:
6 - x = 1 - 7x

3. Get rid of the variables by isolating x on one side:
Move the terms with x to the left side:
-x + 7x = 1 - 6

Combine like terms:
6x = -5

4. Solve for x by dividing both sides by 6:
x = -5/6

Therefore, the solution to the equation is x = -5/6.

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