Solve 62/3/x-8=-4.2*5/7-3

$$\frac{ 6 \frac{ 2 }{ 3 } }{ x } -8 = -4.2 \times \frac{ 5 }{ 7 } -3$$

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7x, the least common multiple of x,7.

$$7\times \frac{6\times 3+2}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Multiply 6 and 3 to get 18.

$$7\times \frac{18+2}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Add 18 and 2 to get 20.

$$7\times \frac{20}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Express 7\times \frac{20}{3} as a single fraction.

$$\frac{7\times 20}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Multiply 7 and 20 to get 140.

$$\frac{140}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Multiply 7 and -8 to get -56.

$$\frac{140}{3}-56x=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Convert decimal number -4.2 to fraction -\frac{42}{10}. Reduce the fraction -\frac{42}{10} to lowest terms by extracting and canceling out 2.

$$\frac{140}{3}-56x=-\frac{21}{5}\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Multiply -\frac{21}{5} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{140}{3}-56x=\frac{-21\times 5}{5\times 7}\times 7x+7x\left(-3\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{140}{3}-56x=\frac{-21}{7}\times 7x+7x\left(-3\right)$$

Divide -21 by 7 to get -3.

$$\frac{140}{3}-56x=-3\times 7x+7x\left(-3\right)$$

Multiply -3 and 7 to get -21.

$$\frac{140}{3}-56x=-21x+7x\left(-3\right)$$

Multiply 7 and -3 to get -21.

$$\frac{140}{3}-56x=-21x-21x$$

Combine -21x and -21x to get -42x.

$$\frac{140}{3}-56x=-42x$$

Add 42x to both sides.

$$\frac{140}{3}-56x+42x=0$$

Combine -56x and 42x to get -14x.

$$\frac{140}{3}-14x=0$$

Subtract \frac{140}{3} from both sides. Anything subtracted from zero gives its negation.

$$-14x=-\frac{140}{3}$$

Divide both sides by -14.

$$x=\frac{-\frac{140}{3}}{-14}$$

Express \frac{-\frac{140}{3}}{-14} as a single fraction.

$$x=\frac{-140}{3\left(-14\right)}$$

Multiply 3 and -14 to get -42.

$$x=\frac{-140}{-42}$$

Reduce the fraction \frac{-140}{-42} to lowest terms by extracting and canceling out -14.

$$x=\frac{10}{3}$$