Solve 40/56x+(2.3-1.0-x)*40/14=2.0*40/100

$$\frac { 40 } { 56 } x + ( 2.3 - 1.0 - x ) \times \frac { 40 } { 14 } = 2.0 \times \frac { 40 } { 100 }$$

Solve for x

$$x=1.36$$

Steps for Solving Linear Equation

Reduce the fraction \frac{40}{56} to lowest terms by extracting and canceling out 8.

$$\frac{5}{7}x+\left(2.3-1-x\right)\times \frac{40}{14}=2\times \frac{40}{100}$$

Subtract 1 from 2.3 to get 1.3.

$$\frac{5}{7}x+\left(1.3-x\right)\times \frac{40}{14}=2\times \frac{40}{100}$$

Reduce the fraction \frac{40}{14} to lowest terms by extracting and canceling out 2.

$$\frac{5}{7}x+\left(1.3-x\right)\times \frac{20}{7}=2\times \frac{40}{100}$$

Use the distributive property to multiply 1.3-x by \frac{20}{7}.

$$\frac{5}{7}x+1.3\times \frac{20}{7}-x\times \frac{20}{7}=2\times \frac{40}{100}$$

Convert decimal number 1.3 to fraction \frac{13}{10}.

$$\frac{5}{7}x+\frac{13}{10}\times \frac{20}{7}-x\times \frac{20}{7}=2\times \frac{40}{100}$$

Multiply \frac{13}{10} times \frac{20}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{7}x+\frac{13\times 20}{10\times 7}-x\times \frac{20}{7}=2\times \frac{40}{100}$$

Do the multiplications in the fraction \frac{13\times 20}{10\times 7}.

$$\frac{5}{7}x+\frac{260}{70}-x\times \frac{20}{7}=2\times \frac{40}{100}$$

Reduce the fraction \frac{260}{70} to lowest terms by extracting and canceling out 10.

$$\frac{5}{7}x+\frac{26}{7}-x\times \frac{20}{7}=2\times \frac{40}{100}$$

Multiply -1 and \frac{20}{7} to get -\frac{20}{7}.

$$\frac{5}{7}x+\frac{26}{7}-\frac{20}{7}x=2\times \frac{40}{100}$$

Combine \frac{5}{7}x and -\frac{20}{7}x to get -\frac{15}{7}x.

$$-\frac{15}{7}x+\frac{26}{7}=2\times \frac{40}{100}$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$-\frac{15}{7}x+\frac{26}{7}=2\times \frac{2}{5}$$

Express 2\times \frac{2}{5} as a single fraction.

$$-\frac{15}{7}x+\frac{26}{7}=\frac{2\times 2}{5}$$

Multiply 2 and 2 to get 4.

$$-\frac{15}{7}x+\frac{26}{7}=\frac{4}{5}$$

Subtract \frac{26}{7} from both sides.

$$-\frac{15}{7}x=\frac{4}{5}-\frac{26}{7}$$

Least common multiple of 5 and 7 is 35. Convert \frac{4}{5} and \frac{26}{7} to fractions with denominator 35.

$$-\frac{15}{7}x=\frac{28}{35}-\frac{130}{35}$$

Since \frac{28}{35} and \frac{130}{35} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{15}{7}x=\frac{28-130}{35}$$

Subtract 130 from 28 to get -102.

$$-\frac{15}{7}x=-\frac{102}{35}$$

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

$$x=-\frac{102}{35}\left(-\frac{7}{15}\right)$$

Multiply -\frac{102}{35} times -\frac{7}{15} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-102\left(-7\right)}{35\times 15}$$

Do the multiplications in the fraction \frac{-102\left(-7\right)}{35\times 15}.

$$x=\frac{714}{525}$$

Reduce the fraction \frac{714}{525} to lowest terms by extracting and canceling out 21.

$$x=\frac{34}{25}$$