Solve 3(x-1)/0.2-2.5=0.4-2x/0.5-7.5

$$\frac { 3 ( x - 1 ) } { 0.2 } - 2.5 = \frac { 0.4 - 2 x } { 0.5 } - 7.5$$

Solve for x

$$x=\frac{54}{95}\approx 0.568421053$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by x-1.

$$\frac{3x-3}{0.2}-2.5=\frac{0.4-2x}{0.5}-7.5$$

Divide each term of 3x-3 by 0.2 to get \frac{3x}{0.2}+\frac{-3}{0.2}.

$$\frac{3x}{0.2}+\frac{-3}{0.2}-2.5=\frac{0.4-2x}{0.5}-7.5$$

Divide 3x by 0.2 to get 15x.

$$15x+\frac{-3}{0.2}-2.5=\frac{0.4-2x}{0.5}-7.5$$

Expand \frac{-3}{0.2} by multiplying both numerator and the denominator by 10.

$$15x+\frac{-30}{2}-2.5=\frac{0.4-2x}{0.5}-7.5$$

Divide -30 by 2 to get -15.

$$15x-15-2.5=\frac{0.4-2x}{0.5}-7.5$$

Subtract 2.5 from -15 to get -17.5.

$$15x-17.5=\frac{0.4-2x}{0.5}-7.5$$

Divide each term of 0.4-2x by 0.5 to get \frac{0.4}{0.5}+\frac{-2x}{0.5}.

$$15x-17.5=\frac{0.4}{0.5}+\frac{-2x}{0.5}-7.5$$

Expand \frac{0.4}{0.5} by multiplying both numerator and the denominator by 10.

$$15x-17.5=\frac{4}{5}+\frac{-2x}{0.5}-7.5$$

Divide -2x by 0.5 to get -4x.

$$15x-17.5=\frac{4}{5}-4x-7.5$$

Convert decimal number 7.5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$15x-17.5=\frac{4}{5}-4x-\frac{15}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{4}{5} and \frac{15}{2} to fractions with denominator 10.

$$15x-17.5=\frac{8}{10}-4x-\frac{75}{10}$$

Since \frac{8}{10} and \frac{75}{10} have the same denominator, subtract them by subtracting their numerators.

$$15x-17.5=\frac{8-75}{10}-4x$$

Subtract 75 from 8 to get -67.

$$15x-17.5=-\frac{67}{10}-4x$$

Add 4x to both sides.

$$15x-17.5+4x=-\frac{67}{10}$$

Combine 15x and 4x to get 19x.

$$19x-17.5=-\frac{67}{10}$$

Add 17.5 to both sides.

$$19x=-\frac{67}{10}+17.5$$

Convert decimal number 17.5 to fraction \frac{175}{10}. Reduce the fraction \frac{175}{10} to lowest terms by extracting and canceling out 5.

$$19x=-\frac{67}{10}+\frac{35}{2}$$

Least common multiple of 10 and 2 is 10. Convert -\frac{67}{10} and \frac{35}{2} to fractions with denominator 10.

$$19x=-\frac{67}{10}+\frac{175}{10}$$

Since -\frac{67}{10} and \frac{175}{10} have the same denominator, add them by adding their numerators.

$$19x=\frac{-67+175}{10}$$

Add -67 and 175 to get 108.

$$19x=\frac{108}{10}$$

Reduce the fraction \frac{108}{10} to lowest terms by extracting and canceling out 2.

$$19x=\frac{54}{5}$$

Divide both sides by 19.

$$x=\frac{\frac{54}{5}}{19}$$

Express \frac{\frac{54}{5}}{19} as a single fraction.

$$x=\frac{54}{5\times 19}$$

Multiply 5 and 19 to get 95.

$$x=\frac{54}{95}$$