2x - {3x - 2[x -(1 - x)]}?

Question

simplify please!

Answer 1

Thanks for adding all of the parentheses.  Start with the innermost set of parentheses.  In this case (1 - x).  Use the distributive property to distribute -1.

2x - {3x - 2[x - (1 - x)]} =

2x - {3x - 2[x + (-1)*(1 - x)]} =

2x - {3x - 2[x + (-1)*(1) - (-1)*(x)]} =

2x - {3x - 2[x + (-1) - (-x)]} =

2x - {3x - 2[x - 1 + x]} =

2x - {3x - 2[2x - 1]} =

Now look at the next innermost parentheses.  In this case [2x - 1].  Use the distributive property to distribute -2.

2x - {3x - 2[2x - 1]} =

2x - {3x + (-2)*[2x - 1]} =

2x - {3x + (-2)*(2x) - (-2)*(1)} =

2x - {3x + (-4x) - (-2)} =

Combine like terms.

2x - {3x - 4x + 2} =

2x - {-x + 2} =

2x - {2 - x} =

Finally use the distributive property to distribute (-1)

2x + (-1)*{2 - x} =

2x + (-1)*(2) - (-1)*(x) =

2x + (-2) - (-x) =

2x - 2 + x =

3x - 2

Hope this helps you!