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 using the properties of equality, we will follow these steps:

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

Step 2: Simplify the expression using the distributive property:
6 - 12x/2 + 5x = 1 - 7x

Step 3: Simplify the expression further by dividing 12x by 2:
6 - 6x + 5x = 1 - 7x

Step 4: Combine like terms on both sides of the equation:
-6x + 5x + 7x = 1 - 6

Step 5: Simplify the expression by adding and subtracting like terms:
6x = -5

Step 6: Divide both sides of the equation by 6 to solve for x:
x = -5/6

Therefore, the equation 3/2(4−8x)+5x=1−7x has a single solution, which is x = -5/6.