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

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

Solve for x

$$x = \frac{44}{17} = 2\frac{10}{17} \approx 2.588235294$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{5} by 2-x.

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

Express \frac{3}{5}\times 2 as a single fraction.

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

Multiply 3 and 2 to get 6.

$$\frac{6}{5}+\frac{3}{5}\left(-1\right)x=\frac{1}{4}\left(x-4\right)$$

Multiply \frac{3}{5} and -1 to get -\frac{3}{5}.

$$\frac{6}{5}-\frac{3}{5}x=\frac{1}{4}\left(x-4\right)$$

Use the distributive property to multiply \frac{1}{4} by x-4.

$$\frac{6}{5}-\frac{3}{5}x=\frac{1}{4}x+\frac{1}{4}\left(-4\right)$$

Multiply \frac{1}{4} and -4 to get \frac{-4}{4}.

$$\frac{6}{5}-\frac{3}{5}x=\frac{1}{4}x+\frac{-4}{4}$$

Divide -4 by 4 to get -1.

$$\frac{6}{5}-\frac{3}{5}x=\frac{1}{4}x-1$$

Subtract \frac{1}{4}x from both sides.

$$\frac{6}{5}-\frac{3}{5}x-\frac{1}{4}x=-1$$

Combine -\frac{3}{5}x and -\frac{1}{4}x to get -\frac{17}{20}x.

$$\frac{6}{5}-\frac{17}{20}x=-1$$

Subtract \frac{6}{5} from both sides.

$$-\frac{17}{20}x=-1-\frac{6}{5}$$

Convert -1 to fraction -\frac{5}{5}.

$$-\frac{17}{20}x=-\frac{5}{5}-\frac{6}{5}$$

Since -\frac{5}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{17}{20}x=\frac{-5-6}{5}$$

Subtract 6 from -5 to get -11.

$$-\frac{17}{20}x=-\frac{11}{5}$$

Multiply both sides by -\frac{20}{17}, the reciprocal of -\frac{17}{20}.

$$x=-\frac{11}{5}\left(-\frac{20}{17}\right)$$

Multiply -\frac{11}{5} times -\frac{20}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\left(-20\right)}{5\times 17}$$

Do the multiplications in the fraction \frac{-11\left(-20\right)}{5\times 17}.

$$x=\frac{220}{85}$$

Reduce the fraction \frac{220}{85} to lowest terms by extracting and canceling out 5.

$$x=\frac{44}{17}$$