Solve 45*1.5%+45*0.03%50%x=x-40

$$45 \times 1.5 \% +45 \times 0.03 \% 50 \% x=x-40$$

Solve for x

$$x = \frac{162700}{3973} = 40\frac{3780}{3973} \approx 40.951422099$$

Steps for Solving Linear Equation

Expand \frac{1.5}{100} by multiplying both numerator and the denominator by 10.

$$45\times \frac{15}{1000}+45\times \frac{0.03}{100}\times \frac{50}{100}x=x-40$$

Reduce the fraction \frac{15}{1000} to lowest terms by extracting and canceling out 5.

$$45\times \frac{3}{200}+45\times \frac{0.03}{100}\times \frac{50}{100}x=x-40$$

Express 45\times \frac{3}{200} as a single fraction.

$$\frac{45\times 3}{200}+45\times \frac{0.03}{100}\times \frac{50}{100}x=x-40$$

Multiply 45 and 3 to get 135.

$$\frac{135}{200}+45\times \frac{0.03}{100}\times \frac{50}{100}x=x-40$$

Reduce the fraction \frac{135}{200} to lowest terms by extracting and canceling out 5.

$$\frac{27}{40}+45\times \frac{0.03}{100}\times \frac{50}{100}x=x-40$$

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

$$\frac{27}{40}+45\times \frac{3}{10000}\times \frac{50}{100}x=x-40$$

Express 45\times \frac{3}{10000} as a single fraction.

$$\frac{27}{40}+\frac{45\times 3}{10000}\times \frac{50}{100}x=x-40$$

Multiply 45 and 3 to get 135.

$$\frac{27}{40}+\frac{135}{10000}\times \frac{50}{100}x=x-40$$

Reduce the fraction \frac{135}{10000} to lowest terms by extracting and canceling out 5.

$$\frac{27}{40}+\frac{27}{2000}\times \frac{50}{100}x=x-40$$

Reduce the fraction \frac{50}{100} to lowest terms by extracting and canceling out 50.

$$\frac{27}{40}+\frac{27}{2000}\times \frac{1}{2}x=x-40$$

Multiply \frac{27}{2000} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27}{40}+\frac{27\times 1}{2000\times 2}x=x-40$$

Do the multiplications in the fraction \frac{27\times 1}{2000\times 2}.

$$\frac{27}{40}+\frac{27}{4000}x=x-40$$

Subtract x from both sides.

$$\frac{27}{40}+\frac{27}{4000}x-x=-40$$

Combine \frac{27}{4000}x and -x to get -\frac{3973}{4000}x.

$$\frac{27}{40}-\frac{3973}{4000}x=-40$$

Subtract \frac{27}{40} from both sides.

$$-\frac{3973}{4000}x=-40-\frac{27}{40}$$

Convert -40 to fraction -\frac{1600}{40}.

$$-\frac{3973}{4000}x=-\frac{1600}{40}-\frac{27}{40}$$

Since -\frac{1600}{40} and \frac{27}{40} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3973}{4000}x=\frac{-1600-27}{40}$$

Subtract 27 from -1600 to get -1627.

$$-\frac{3973}{4000}x=-\frac{1627}{40}$$

Multiply both sides by -\frac{4000}{3973}, the reciprocal of -\frac{3973}{4000}.

$$x=-\frac{1627}{40}\left(-\frac{4000}{3973}\right)$$

Multiply -\frac{1627}{40} times -\frac{4000}{3973} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-1627\left(-4000\right)}{40\times 3973}$$

Do the multiplications in the fraction \frac{-1627\left(-4000\right)}{40\times 3973}.

$$x=\frac{6508000}{158920}$$

Reduce the fraction \frac{6508000}{158920} to lowest terms by extracting and canceling out 40.

$$x=\frac{162700}{3973}$$