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

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

Solve for x

$$x = \frac{225}{13} = 17\frac{4}{13} \approx 17.307692308$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,3,2,4.

$$12x-60\left(\frac{2}{3}x-\left(\frac{1-x}{2}+4\right)\right)=45\left(1-x\right)$$

To find the opposite of \frac{1-x}{2}+4, find the opposite of each term.

$$12x-60\left(\frac{2}{3}x-\frac{1-x}{2}-4\right)=45\left(1-x\right)$$

Use the distributive property to multiply 45 by 1-x.

$$12x-60\left(\frac{2}{3}x-\frac{1-x}{2}-4\right)=45-45x$$

Divide each term of 1-x by 2 to get \frac{1}{2}-\frac{1}{2}x.

$$12x-60\left(\frac{2}{3}x-\left(\frac{1}{2}-\frac{1}{2}x\right)-4\right)=45-45x$$

To find the opposite of \frac{1}{2}-\frac{1}{2}x, find the opposite of each term.

$$12x-60\left(\frac{2}{3}x-\frac{1}{2}-\left(-\frac{1}{2}x\right)-4\right)=45-45x$$

The opposite of -\frac{1}{2}x is \frac{1}{2}x.

$$12x-60\left(\frac{2}{3}x-\frac{1}{2}+\frac{1}{2}x-4\right)=45-45x$$

Combine \frac{2}{3}x and \frac{1}{2}x to get \frac{7}{6}x.

$$12x-60\left(\frac{7}{6}x-\frac{1}{2}-4\right)=45-45x$$

Convert 4 to fraction \frac{8}{2}.

$$12x-60\left(\frac{7}{6}x-\frac{1}{2}-\frac{8}{2}\right)=45-45x$$

Since -\frac{1}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$12x-60\left(\frac{7}{6}x+\frac{-1-8}{2}\right)=45-45x$$

Subtract 8 from -1 to get -9.

$$12x-60\left(\frac{7}{6}x-\frac{9}{2}\right)=45-45x$$

Use the distributive property to multiply -60 by \frac{7}{6}x-\frac{9}{2}.

$$12x-60\times \frac{7}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

Express -60\times \frac{7}{6} as a single fraction.

$$12x+\frac{-60\times 7}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

Multiply -60 and 7 to get -420.

$$12x+\frac{-420}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

Divide -420 by 6 to get -70.

$$12x-70x-60\left(-\frac{9}{2}\right)=45-45x$$

Express -60\left(-\frac{9}{2}\right) as a single fraction.

$$12x-70x+\frac{-60\left(-9\right)}{2}=45-45x$$

Multiply -60 and -9 to get 540.

$$12x-70x+\frac{540}{2}=45-45x$$

Divide 540 by 2 to get 270.

$$12x-70x+270=45-45x$$

Combine 12x and -70x to get -58x.

$$-58x+270=45-45x$$

Add 45x to both sides.

$$-58x+270+45x=45$$

Combine -58x and 45x to get -13x.

$$-13x+270=45$$

Subtract 270 from both sides.

$$-13x=45-270$$

Subtract 270 from 45 to get -225.

$$-13x=-225$$

Divide both sides by -13.

$$x=\frac{-225}{-13}$$

Fraction \frac{-225}{-13} can be simplified to \frac{225}{13} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{225}{13}$$