Question

Can someone help me with this question

Answer 1

Answer:

$\frac{2}{3} x + \frac{1}{3} - \frac{1}{3} x = \frac{1}{3} ( x - 1)\\\\ \\\frac{4}{3}x - \frac{4}{3} - \frac{2}{3} = \frac{4}{3} ( x - 1)\\\\( \frac{1}{3} x + \frac{2}{3} ) + ( -\frac{2}{3}x - \frac{4}{3}) = -\frac{1}{3} ( x + 2)\\\\(\frac{2}{3}x + \frac{1}{3} ) + (\frac{2}{3} x - \frac{2}{3} ) = \frac{1}{3} ( 4x - 1 )$

Step-by-step explanation:

Simplify each equation by combining like terms, and then factoring

$\frac{2}{3} x + \frac{1}{3} - \frac{1}{3} x$

= $\frac{1}{3} x + \frac{1}{3}$

= $\frac{1}{3}$ ( x + 1)

$\frac{4}{3}x - \frac{4}{3} - \frac{2}{3}$

= $\frac{4}{3}x - \frac{6}{3}$

= $\frac{4}{3}$ ( x - 1 )

$\ ( \frac{1}{3} x + \frac{2}{3} ) + ( -\frac{2}{3}x - \frac{4}{3})$

=$-\frac{1}{3}x - \frac{2}{3}$

=$- \frac{1}{3} x$ ( x + 2)

$\ (\frac{2}{3}x + \frac{1}{3} ) + (\frac{2}{3} x - \frac{2}{3} )$

= $\ \frac{4}{3}x - \frac{1}{3}$

= $\(\frac{1}{3}$ ( 4x - 1)

Answer 2

Answer:

Step-by-step explanation:

$1)\frac{2}{3}x + \frac{1}{3}-\frac{1}{3}x = \frac{2}{3}x-\frac{1}{3}x +\frac{1}{3}\\\\\\=\frac{(2-1)}{3}x+\frac{1}{3}\\\\\\=\frac{1}{3}x+\frac{1}{3}\\\\\\=\frac{1}{3}(x+1)$

$2) \frac{4}{3}x-\frac{2}{3}-\frac{2}{3}=\frac{4}{3}x + \frac{(-2-2)}{3}$

                    $=\frac{4}{3}x -\frac{4}{3}\\\\\\=\frac{4}{3}(x-1)$

$3) (\frac{1}{3}x+\frac{2}{3})+(\frac{-2}{3}x-\frac{4}{3})=\frac{1}{3}x-\frac{2}{3}x+\frac{2}{3}-\frac{4}{3}$

                                     $= \frac{-1}{3}x-\frac{2}{3}\\\\\\=\frac{-1}{3}(x+2)$

4) $(\frac{2}{3}x +\frac{1}{3})+(\frac{2}{3}x-\frac{2}{3})=\frac{2}{3}x+\frac{2}{3}x+\frac{1}{3}-\frac{2}{3}$

                                    $=\frac{4}{3}x-\frac{1}{3}\\\\\\=\frac{1}{3}(4x-1)$