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

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

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3,2.

$$3x-12\left(\frac{2}{3}x-\left(\frac{1-x}{2}+1\right)\right)=9\left(1-x\right)$$

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

$$3x-12\left(\frac{2}{3}x-\frac{1-x}{2}-1\right)=9\left(1-x\right)$$

Use the distributive property to multiply 9 by 1-x.

$$3x-12\left(\frac{2}{3}x-\frac{1-x}{2}-1\right)=9-9x$$

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

$$3x-12\left(\frac{2}{3}x-\left(\frac{1}{2}-\frac{1}{2}x\right)-1\right)=9-9x$$

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

$$3x-12\left(\frac{2}{3}x-\frac{1}{2}-\left(-\frac{1}{2}x\right)-1\right)=9-9x$$

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

$$3x-12\left(\frac{2}{3}x-\frac{1}{2}+\frac{1}{2}x-1\right)=9-9x$$

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

$$3x-12\left(\frac{7}{6}x-\frac{1}{2}-1\right)=9-9x$$

Convert 1 to fraction \frac{2}{2}.

$$3x-12\left(\frac{7}{6}x-\frac{1}{2}-\frac{2}{2}\right)=9-9x$$

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

$$3x-12\left(\frac{7}{6}x+\frac{-1-2}{2}\right)=9-9x$$

Subtract 2 from -1 to get -3.

$$3x-12\left(\frac{7}{6}x-\frac{3}{2}\right)=9-9x$$

Use the distributive property to multiply -12 by \frac{7}{6}x-\frac{3}{2}.

$$3x-12\times \frac{7}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

Express -12\times \frac{7}{6} as a single fraction.

$$3x+\frac{-12\times 7}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

Multiply -12 and 7 to get -84.

$$3x+\frac{-84}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

Divide -84 by 6 to get -14.

$$3x-14x-12\left(-\frac{3}{2}\right)=9-9x$$

Express -12\left(-\frac{3}{2}\right) as a single fraction.

$$3x-14x+\frac{-12\left(-3\right)}{2}=9-9x$$

Multiply -12 and -3 to get 36.

$$3x-14x+\frac{36}{2}=9-9x$$

Divide 36 by 2 to get 18.

$$3x-14x+18=9-9x$$

Combine 3x and -14x to get -11x.

$$-11x+18=9-9x$$

Add 9x to both sides.

$$-11x+18+9x=9$$

Combine -11x and 9x to get -2x.

$$-2x+18=9$$

Subtract 18 from both sides.

$$-2x=9-18$$

Subtract 18 from 9 to get -9.

$$-2x=-9$$

Divide both sides by -2.

$$x=\frac{-9}{-2}$$

Fraction \frac{-9}{-2} can be simplified to \frac{9}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{2}$$