Solve 3(1-x)+2x=2/5(-2x+4/10)

$$3(1-x)+2x= \frac{ 2 }{ 5 } (-2x+ \frac{ 4 }{ 10 } )$$

Solve for x

$$x = \frac{71}{5} = 14\frac{1}{5} = 14.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 1-x.

$$3-3x+2x=\frac{2}{5}\left(-2x+\frac{4}{10}\right)$$

Combine -3x and 2x to get -x.

$$3-x=\frac{2}{5}\left(-2x+\frac{4}{10}\right)$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$3-x=\frac{2}{5}\left(-2x+\frac{2}{5}\right)$$

Use the distributive property to multiply \frac{2}{5} by -2x+\frac{2}{5}.

$$3-x=\frac{2}{5}\left(-2\right)x+\frac{2}{5}\times \frac{2}{5}$$

Express \frac{2}{5}\left(-2\right) as a single fraction.

$$3-x=\frac{2\left(-2\right)}{5}x+\frac{2}{5}\times \frac{2}{5}$$

Multiply 2 and -2 to get -4.

$$3-x=\frac{-4}{5}x+\frac{2}{5}\times \frac{2}{5}$$

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

$$3-x=-\frac{4}{5}x+\frac{2}{5}\times \frac{2}{5}$$

Multiply \frac{2}{5} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$3-x=-\frac{4}{5}x+\frac{2\times 2}{5\times 5}$$

Do the multiplications in the fraction \frac{2\times 2}{5\times 5}.

$$3-x=-\frac{4}{5}x+\frac{4}{25}$$

Add \frac{4}{5}x to both sides.

$$3-x+\frac{4}{5}x=\frac{4}{25}$$

Combine -x and \frac{4}{5}x to get -\frac{1}{5}x.

$$3-\frac{1}{5}x=\frac{4}{25}$$

Subtract 3 from both sides.

$$-\frac{1}{5}x=\frac{4}{25}-3$$

Convert 3 to fraction \frac{75}{25}.

$$-\frac{1}{5}x=\frac{4}{25}-\frac{75}{25}$$

Since \frac{4}{25} and \frac{75}{25} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{5}x=\frac{4-75}{25}$$

Subtract 75 from 4 to get -71.

$$-\frac{1}{5}x=-\frac{71}{25}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}.

$$x=-\frac{71}{25}\left(-5\right)$$

Express -\frac{71}{25}\left(-5\right) as a single fraction.

$$x=\frac{-71\left(-5\right)}{25}$$

Multiply -71 and -5 to get 355.

$$x=\frac{355}{25}$$

Reduce the fraction \frac{355}{25} to lowest terms by extracting and canceling out 5.

$$x=\frac{71}{5}$$