Solve 10*0.006/3=3/2*10^-2+29/M*10^-2

$$\frac { 10 \times 0.006 } { 3 } = \frac { 3 } { 2 } \times 10 ^ { - 2 } + \frac { 29 } { M } \times 10 ^ { - 2 }$$

Solve for M

$$M=58$$

Steps for Solving Linear Equation

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6M, the least common multiple of 3,2,M.

$$2M\times 10\times 0.006=\frac{3}{2}\times 10^{-2}\times 6M+6\times 29\times 10^{-2}$$

Multiply 2 and 10 to get 20.

$$20M\times 0.006=\frac{3}{2}\times 10^{-2}\times 6M+6\times 29\times 10^{-2}$$

Multiply 20 and 0.006 to get 0.12.

$$0.12M=\frac{3}{2}\times 10^{-2}\times 6M+6\times 29\times 10^{-2}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$0.12M=\frac{3}{2}\times \frac{1}{100}\times 6M+6\times 29\times 10^{-2}$$

Multiply \frac{3}{2} and \frac{1}{100} to get \frac{3}{200}.

$$0.12M=\frac{3}{200}\times 6M+6\times 29\times 10^{-2}$$

Multiply \frac{3}{200} and 6 to get \frac{9}{100}.

$$0.12M=\frac{9}{100}M+6\times 29\times 10^{-2}$$

Multiply 6 and 29 to get 174.

$$0.12M=\frac{9}{100}M+174\times 10^{-2}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$0.12M=\frac{9}{100}M+174\times \frac{1}{100}$$

Multiply 174 and \frac{1}{100} to get \frac{87}{50}.

$$0.12M=\frac{9}{100}M+\frac{87}{50}$$

Subtract \frac{9}{100}M from both sides.

$$0.12M-\frac{9}{100}M=\frac{87}{50}$$

Combine 0.12M and -\frac{9}{100}M to get \frac{3}{100}M.

$$\frac{3}{100}M=\frac{87}{50}$$

Multiply both sides by \frac{100}{3}, the reciprocal of \frac{3}{100}.

$$M=\frac{87}{50}\times \frac{100}{3}$$

Multiply \frac{87}{50} and \frac{100}{3} to get 58.

$$M=58$$