Question

is (-1/2 x + 6/7) - (7/2 x - 4/7) equivalent to -4 x + 2/7 ? use the properties of operations to justify your answer

Answer 1

Answer:

The given equation is NOT justified.

Step-by-step explanation:

Here, the given equation is $(\frac{-1}{2}x + \frac{6}{7} ) - (\frac{7}{2}x - \frac{4}{7} )$   = $-4x + \frac{2}{7}$

Now, here Consider the left hand side and simplifying the left side by operating on the like terms,

⇒$(\frac{-1}{2}x + \frac{6}{7} ) - (\frac{7}{2}x - \frac{4}{7} )$   = $\frac{-1}{2}x + \frac{6}{7} - \frac{7}{2}x + \frac{4}{7} = (\frac{-1}{2}x -\frac{7}{2}x) + (\frac{6}{7} + \frac{4}{7})$

=$(\frac{-1 - 7}{2}x ) + (\frac{6 + 4}{7} ) = \frac{-8x}{2} + \frac{10}{7} \neq -4x + \frac{2}{7}$

Here, Left side of equation  ≠ Right side of the equation

Hence, $(\frac{-1}{2}x + \frac{6}{7} ) - (\frac{7}{2}x - \frac{4}{7} )$   ≠ $-4x + \frac{2}{7}$