Solve (5x-2)*3%=(7x+8)*20%

$$( 5 x - 2 ) \times 3 \% = ( 7 x + 8 ) \times 20 \%$$

Solve for x

$$x = -\frac{166}{125} = -1\frac{41}{125} = -1.328$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x-2 by \frac{3}{100}.

$$5x\times \frac{3}{100}-2\times \frac{3}{100}=\left(7x+8\right)\times \frac{20}{100}$$

Express 5\times \frac{3}{100} as a single fraction.

$$\frac{5\times 3}{100}x-2\times \frac{3}{100}=\left(7x+8\right)\times \frac{20}{100}$$

Multiply 5 and 3 to get 15.

$$\frac{15}{100}x-2\times \frac{3}{100}=\left(7x+8\right)\times \frac{20}{100}$$

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{3}{20}x-2\times \frac{3}{100}=\left(7x+8\right)\times \frac{20}{100}$$

Express -2\times \frac{3}{100} as a single fraction.

$$\frac{3}{20}x+\frac{-2\times 3}{100}=\left(7x+8\right)\times \frac{20}{100}$$

Multiply -2 and 3 to get -6.

$$\frac{3}{20}x+\frac{-6}{100}=\left(7x+8\right)\times \frac{20}{100}$$

Reduce the fraction \frac{-6}{100} to lowest terms by extracting and canceling out 2.

$$\frac{3}{20}x-\frac{3}{50}=\left(7x+8\right)\times \frac{20}{100}$$

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

$$\frac{3}{20}x-\frac{3}{50}=\left(7x+8\right)\times \frac{1}{5}$$

Use the distributive property to multiply 7x+8 by \frac{1}{5}.

$$\frac{3}{20}x-\frac{3}{50}=7x\times \frac{1}{5}+8\times \frac{1}{5}$$

Multiply 7 and \frac{1}{5} to get \frac{7}{5}.

$$\frac{3}{20}x-\frac{3}{50}=\frac{7}{5}x+8\times \frac{1}{5}$$

Multiply 8 and \frac{1}{5} to get \frac{8}{5}.

$$\frac{3}{20}x-\frac{3}{50}=\frac{7}{5}x+\frac{8}{5}$$

Subtract \frac{7}{5}x from both sides.

$$\frac{3}{20}x-\frac{3}{50}-\frac{7}{5}x=\frac{8}{5}$$

Combine \frac{3}{20}x and -\frac{7}{5}x to get -\frac{5}{4}x.

$$-\frac{5}{4}x-\frac{3}{50}=\frac{8}{5}$$

Add \frac{3}{50} to both sides.

$$-\frac{5}{4}x=\frac{8}{5}+\frac{3}{50}$$

Least common multiple of 5 and 50 is 50. Convert \frac{8}{5} and \frac{3}{50} to fractions with denominator 50.

$$-\frac{5}{4}x=\frac{80}{50}+\frac{3}{50}$$

Since \frac{80}{50} and \frac{3}{50} have the same denominator, add them by adding their numerators.

$$-\frac{5}{4}x=\frac{80+3}{50}$$

Add 80 and 3 to get 83.

$$-\frac{5}{4}x=\frac{83}{50}$$

Multiply both sides by -\frac{4}{5}, the reciprocal of -\frac{5}{4}.

$$x=\frac{83}{50}\left(-\frac{4}{5}\right)$$

Multiply \frac{83}{50} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{83\left(-4\right)}{50\times 5}$$

Do the multiplications in the fraction \frac{83\left(-4\right)}{50\times 5}.

$$x=\frac{-332}{250}$$

Reduce the fraction \frac{-332}{250} to lowest terms by extracting and canceling out 2.

$$x=-\frac{166}{125}$$