Solve (x-3/10)*8/7=(105-x)+3/10

$$(x- \frac{ 3 }{ 10 } ) \times \frac{ 8 }{ 7 } =(105-x)+ \frac{ 3 }{ 10 }$$

Solve for x

$$x = \frac{493}{10} = 49\frac{3}{10} = 49.3$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-\frac{3}{10} by \frac{8}{7}.

$$x\times \frac{8}{7}-\frac{3}{10}\times \frac{8}{7}=105-x+\frac{3}{10}$$

Multiply -\frac{3}{10} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$x\times \frac{8}{7}+\frac{-3\times 8}{10\times 7}=105-x+\frac{3}{10}$$

Do the multiplications in the fraction \frac{-3\times 8}{10\times 7}.

$$x\times \frac{8}{7}+\frac{-24}{70}=105-x+\frac{3}{10}$$

Reduce the fraction \frac{-24}{70} to lowest terms by extracting and canceling out 2.

$$x\times \frac{8}{7}-\frac{12}{35}=105-x+\frac{3}{10}$$

Convert 105 to fraction \frac{1050}{10}.

$$x\times \frac{8}{7}-\frac{12}{35}=\frac{1050}{10}-x+\frac{3}{10}$$

Since \frac{1050}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$x\times \frac{8}{7}-\frac{12}{35}=\frac{1050+3}{10}-x$$

Add 1050 and 3 to get 1053.

$$x\times \frac{8}{7}-\frac{12}{35}=\frac{1053}{10}-x$$

Add x to both sides.

$$x\times \frac{8}{7}-\frac{12}{35}+x=\frac{1053}{10}$$

Combine x\times \frac{8}{7} and x to get \frac{15}{7}x.

$$\frac{15}{7}x-\frac{12}{35}=\frac{1053}{10}$$

Add \frac{12}{35} to both sides.

$$\frac{15}{7}x=\frac{1053}{10}+\frac{12}{35}$$

Least common multiple of 10 and 35 is 70. Convert \frac{1053}{10} and \frac{12}{35} to fractions with denominator 70.

$$\frac{15}{7}x=\frac{7371}{70}+\frac{24}{70}$$

Since \frac{7371}{70} and \frac{24}{70} have the same denominator, add them by adding their numerators.

$$\frac{15}{7}x=\frac{7371+24}{70}$$

Add 7371 and 24 to get 7395.

$$\frac{15}{7}x=\frac{7395}{70}$$

Reduce the fraction \frac{7395}{70} to lowest terms by extracting and canceling out 5.

$$\frac{15}{7}x=\frac{1479}{14}$$

Multiply both sides by \frac{7}{15}, the reciprocal of \frac{15}{7}.

$$x=\frac{1479}{14}\times \frac{7}{15}$$

Multiply \frac{1479}{14} times \frac{7}{15} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1479\times 7}{14\times 15}$$

Do the multiplications in the fraction \frac{1479\times 7}{14\times 15}.

$$x=\frac{10353}{210}$$

Reduce the fraction \frac{10353}{210} to lowest terms by extracting and canceling out 21.

$$x=\frac{493}{10}$$