Solve 62/3/x-8=-42*5/7-3

$$\frac{ 6 \frac{ 2 }{ 3 } }{ x } -8 = -42 \times \frac{ 5 }{ 7 } -3$$

Solve for x

$$x=-\frac{4}{15}\approx -0.266666667$$

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.

$$7\times \frac{6\times 3+2}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Multiply 6 and 3 to get 18.

$$7\times \frac{18+2}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Add 18 and 2 to get 20.

$$7\times \frac{20}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

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

$$\frac{7\times 20}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Multiply 7 and 20 to get 140.

$$\frac{140}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Multiply 7 and -8 to get -56.

$$\frac{140}{3}-56x=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Express -42\times \frac{5}{7} as a single fraction.

$$\frac{140}{3}-56x=\frac{-42\times 5}{7}\times 7x+7x\left(-3\right)$$

Multiply -42 and 5 to get -210.

$$\frac{140}{3}-56x=\frac{-210}{7}\times 7x+7x\left(-3\right)$$

Divide -210 by 7 to get -30.

$$\frac{140}{3}-56x=-30\times 7x+7x\left(-3\right)$$

Multiply -30 and 7 to get -210.

$$\frac{140}{3}-56x=-210x+7x\left(-3\right)$$

Multiply 7 and -3 to get -21.

$$\frac{140}{3}-56x=-210x-21x$$

Combine -210x and -21x to get -231x.

$$\frac{140}{3}-56x=-231x$$

Add 231x to both sides.

$$\frac{140}{3}-56x+231x=0$$

Combine -56x and 231x to get 175x.

$$\frac{140}{3}+175x=0$$

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

$$175x=-\frac{140}{3}$$

Divide both sides by 175.

$$x=\frac{-\frac{140}{3}}{175}$$

Express \frac{-\frac{140}{3}}{175} as a single fraction.

$$x=\frac{-140}{3\times 175}$$

Multiply 3 and 175 to get 525.

$$x=\frac{-140}{525}$$

Reduce the fraction \frac{-140}{525} to lowest terms by extracting and canceling out 35.

$$x=-\frac{4}{15}$$