Solve 2/5(2-x)=7/4(x-4)

$$\frac { 2 } { 5 } ( 2 - x ) = \frac { 7 } { 4 } ( x - 4 )$$

Solve for x

$$x = \frac{156}{43} = 3\frac{27}{43} \approx 3.627906977$$

Steps for Solving Linear Equation

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

$$\frac{2}{5}\times 2+\frac{2}{5}\left(-1\right)x=\frac{7}{4}\left(x-4\right)$$

Express \frac{2}{5}\times 2 as a single fraction.

$$\frac{2\times 2}{5}+\frac{2}{5}\left(-1\right)x=\frac{7}{4}\left(x-4\right)$$

Multiply 2 and 2 to get 4.

$$\frac{4}{5}+\frac{2}{5}\left(-1\right)x=\frac{7}{4}\left(x-4\right)$$

Multiply \frac{2}{5} and -1 to get -\frac{2}{5}.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}\left(x-4\right)$$

Use the distributive property to multiply \frac{7}{4} by x-4.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x+\frac{7}{4}\left(-4\right)$$

Express \frac{7}{4}\left(-4\right) as a single fraction.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x+\frac{7\left(-4\right)}{4}$$

Multiply 7 and -4 to get -28.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x+\frac{-28}{4}$$

Divide -28 by 4 to get -7.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x-7$$

Subtract \frac{7}{4}x from both sides.

$$\frac{4}{5}-\frac{2}{5}x-\frac{7}{4}x=-7$$

Combine -\frac{2}{5}x and -\frac{7}{4}x to get -\frac{43}{20}x.

$$\frac{4}{5}-\frac{43}{20}x=-7$$

Subtract \frac{4}{5} from both sides.

$$-\frac{43}{20}x=-7-\frac{4}{5}$$

Convert -7 to fraction -\frac{35}{5}.

$$-\frac{43}{20}x=-\frac{35}{5}-\frac{4}{5}$$

Since -\frac{35}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{43}{20}x=\frac{-35-4}{5}$$

Subtract 4 from -35 to get -39.

$$-\frac{43}{20}x=-\frac{39}{5}$$

Multiply both sides by -\frac{20}{43}, the reciprocal of -\frac{43}{20}.

$$x=-\frac{39}{5}\left(-\frac{20}{43}\right)$$

Multiply -\frac{39}{5} times -\frac{20}{43} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-39\left(-20\right)}{5\times 43}$$

Do the multiplications in the fraction \frac{-39\left(-20\right)}{5\times 43}.

$$x=\frac{780}{215}$$

Reduce the fraction \frac{780}{215} to lowest terms by extracting and canceling out 5.

$$x=\frac{156}{43}$$