$$\frac { 2 } { 7 } x + \frac { 1 } { 2 } x = \frac { 1 } { 4 } - x + 1$$
$x=\frac{7}{10}=0.7$
$$\frac{11}{14}x=\frac{1}{4}-x+1$$
$$\frac{11}{14}x=\frac{1}{4}-x+\frac{4}{4}$$
$$\frac{11}{14}x=\frac{1+4}{4}-x$$
$$\frac{11}{14}x=\frac{5}{4}-x$$
$$\frac{11}{14}x+x=\frac{5}{4}$$
$$\frac{25}{14}x=\frac{5}{4}$$
$$x=\frac{5}{4}\times \frac{14}{25}$$
$$x=\frac{5\times 14}{4\times 25}$$
$$x=\frac{70}{100}$$
$$x=\frac{7}{10}$$
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