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

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

Solve for x

$$x=-\frac{9}{20}=-0.45$$

Steps for Solving Linear Equation

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

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

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

$$\frac{1}{3}x+\frac{8}{2}-\frac{3}{2}=-3x+1$$

Since \frac{8}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}x+\frac{8-3}{2}=-3x+1$$

Subtract 3 from 8 to get 5.

$$\frac{1}{3}x+\frac{5}{2}=-3x+1$$

Add 3x to both sides.

$$\frac{1}{3}x+\frac{5}{2}+3x=1$$

Combine \frac{1}{3}x and 3x to get \frac{10}{3}x.

$$\frac{10}{3}x+\frac{5}{2}=1$$

Subtract \frac{5}{2} from both sides.

$$\frac{10}{3}x=1-\frac{5}{2}$$

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

$$\frac{10}{3}x=\frac{2}{2}-\frac{5}{2}$$

Since \frac{2}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}x=\frac{2-5}{2}$$

Subtract 5 from 2 to get -3.

$$\frac{10}{3}x=-\frac{3}{2}$$

Multiply both sides by \frac{3}{10}, the reciprocal of \frac{10}{3}.

$$x=-\frac{3}{2}\times \frac{3}{10}$$

Multiply -\frac{3}{2} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-3\times 3}{2\times 10}$$

Do the multiplications in the fraction \frac{-3\times 3}{2\times 10}.

$$x=\frac{-9}{20}$$

Fraction \frac{-9}{20} can be rewritten as -\frac{9}{20} by extracting the negative sign.

$$x=-\frac{9}{20}$$