Solve 4x+0.8/0.6-0.03x+0.04/0.03=x-1/3

$$\frac { 4 x + 0.8 } { 0.6 } - \frac { 0.03 x + 0.04 } { 0.03 } = \frac { x - 1 } { 3 }$$

Solve for x

$$x=-0.0625$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3\times \frac{4x+0.8}{0.6}-3\times \frac{0.03x+0.04}{0.03}=x-1$$

Divide each term of 4x+0.8 by 0.6 to get \frac{4x}{0.6}+\frac{0.8}{0.6}.

$$3\left(\frac{4x}{0.6}+\frac{0.8}{0.6}\right)-3\times \frac{0.03x+0.04}{0.03}=x-1$$

Divide 4x by 0.6 to get \frac{20}{3}x.

$$3\left(\frac{20}{3}x+\frac{0.8}{0.6}\right)-3\times \frac{0.03x+0.04}{0.03}=x-1$$

Expand \frac{0.8}{0.6} by multiplying both numerator and the denominator by 10.

$$3\left(\frac{20}{3}x+\frac{8}{6}\right)-3\times \frac{0.03x+0.04}{0.03}=x-1$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$3\left(\frac{20}{3}x+\frac{4}{3}\right)-3\times \frac{0.03x+0.04}{0.03}=x-1$$

Use the distributive property to multiply 3 by \frac{20}{3}x+\frac{4}{3}.

$$20x+3\times \frac{4}{3}-3\times \frac{0.03x+0.04}{0.03}=x-1$$

Cancel out 3 and 3.

$$20x+4-3\times \frac{0.03x+0.04}{0.03}=x-1$$

Divide each term of 0.03x+0.04 by 0.03 to get \frac{0.03x}{0.03}+\frac{0.04}{0.03}.

$$20x+4-3\left(\frac{0.03x}{0.03}+\frac{0.04}{0.03}\right)=x-1$$

Cancel out 0.03 and 0.03.

$$20x+4-3\left(x+\frac{0.04}{0.03}\right)=x-1$$

Expand \frac{0.04}{0.03} by multiplying both numerator and the denominator by 100.

$$20x+4-3\left(x+\frac{4}{3}\right)=x-1$$

Use the distributive property to multiply -3 by x+\frac{4}{3}.

$$20x+4-3x-3\times \frac{4}{3}=x-1$$

Multiply -3 times \frac{4}{3}.

$$20x+4-3x-4=x-1$$

Combine 20x and -3x to get 17x.

$$17x+4-4=x-1$$

Subtract 4 from 4 to get 0.

$$17x=x-1$$

Subtract x from both sides.

$$17x-x=-1$$

Combine 17x and -x to get 16x.

$$16x=-1$$

Divide both sides by 16.

$$x=\frac{-1}{16}$$

Fraction \frac{-1}{16} can be rewritten as -\frac{1}{16} by extracting the negative sign.

$$x=-\frac{1}{16}$$