Question

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

Answer 1

To solve the equation \( \frac{3}{2}(4 - 8x) + 5x = 1 - 7x \), first, distribute \( \frac{3}{2} \) to \( 4 - 8x \), giving \( 6 - 12x + 5x = 1 - 7x \) (using the distributive property). Next, combine like terms on the left side to get \( 6 - 7x = 1 - 7x \), and then add \( 7x \) to both sides to isolate constants, resulting in \( 6 = 1 \) (applying the subtraction property of equality). Since \( 6 = 1 \) is a false statement, the equation has no solutions.