Solve 19/18x-[-1/2x-(3/2x+1)-1/3x]=-(frac{4}{2}-2x)

$$\frac { 19 } { 18 } x - [ - \frac { 1 } { 2 } x - ( \frac { 3 } { 2 } x + 1 ) - \frac { 1 } { 3 } x ] = - ( \frac { 4 } { 2 } - 2 x )$$

Solve for x

$$x = -\frac{54}{25} = -2\frac{4}{25} = -2.16$$

Steps for Solving Linear Equation

To find the opposite of \frac{3}{2}x+1, find the opposite of each term.

$$\frac{19}{18}x-\left(-\frac{1}{2}x-\frac{3}{2}x-1-\frac{1}{3}x\right)=-\left(\frac{4}{2}-2x\right)$$

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

$$\frac{19}{18}x-\left(-2x-1-\frac{1}{3}x\right)=-\left(\frac{4}{2}-2x\right)$$

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

$$\frac{19}{18}x-\left(-\frac{7}{3}x-1\right)=-\left(\frac{4}{2}-2x\right)$$

To find the opposite of -\frac{7}{3}x-1, find the opposite of each term.

$$\frac{19}{18}x-\left(-\frac{7}{3}x\right)-\left(-1\right)=-\left(\frac{4}{2}-2x\right)$$

The opposite of -\frac{7}{3}x is \frac{7}{3}x.

$$\frac{19}{18}x+\frac{7}{3}x-\left(-1\right)=-\left(\frac{4}{2}-2x\right)$$

The opposite of -1 is 1.

$$\frac{19}{18}x+\frac{7}{3}x+1=-\left(\frac{4}{2}-2x\right)$$

Combine \frac{19}{18}x and \frac{7}{3}x to get \frac{61}{18}x.

$$\frac{61}{18}x+1=-\left(\frac{4}{2}-2x\right)$$

Divide 4 by 2 to get 2.

$$\frac{61}{18}x+1=-\left(2-2x\right)$$

To find the opposite of 2-2x, find the opposite of each term.

$$\frac{61}{18}x+1=-2-\left(-2x\right)$$

The opposite of -2x is 2x.

$$\frac{61}{18}x+1=-2+2x$$

Subtract 2x from both sides.

$$\frac{61}{18}x+1-2x=-2$$

Combine \frac{61}{18}x and -2x to get \frac{25}{18}x.

$$\frac{25}{18}x+1=-2$$

Subtract 1 from both sides.

$$\frac{25}{18}x=-2-1$$

Subtract 1 from -2 to get -3.

$$\frac{25}{18}x=-3$$

Multiply both sides by \frac{18}{25}, the reciprocal of \frac{25}{18}.

$$x=-3\times \frac{18}{25}$$

Express -3\times \frac{18}{25} as a single fraction.

$$x=\frac{-3\times 18}{25}$$

Multiply -3 and 18 to get -54.

$$x=\frac{-54}{25}$$

Fraction \frac{-54}{25} can be rewritten as -\frac{54}{25} by extracting the negative sign.

$$x=-\frac{54}{25}$$