Solve 62/3divx-8=-4.25/7-3

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

Solve for x

$$x = \frac{700}{9} = 77\frac{7}{9} \approx 77.777777778$$

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.

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

Multiply 6 and 3 to get 18.

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

Add 18 and 2 to get 20.

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

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

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

Multiply 7 and 20 to get 140.

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

Multiply 7 and -8 to get -56.

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

Multiply 4.2 and 7 to get 29.4.

$$\frac{140}{3}-56x=-x\left(29.4+5\right)+7x\left(-3\right)$$

Add 29.4 and 5 to get 34.4.

$$\frac{140}{3}-56x=-x\times 34.4+7x\left(-3\right)$$

Multiply 7 and -3 to get -21.

$$\frac{140}{3}-56x=-x\times 34.4-21x$$

Add x\times 34.4 to both sides.

$$\frac{140}{3}-56x+x\times 34.4=-21x$$

Combine -56x and x\times 34.4 to get -21.6x.

$$\frac{140}{3}-21.6x=-21x$$

Add 21x to both sides.

$$\frac{140}{3}-21.6x+21x=0$$

Combine -21.6x and 21x to get -0.6x.

$$\frac{140}{3}-0.6x=0$$

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

$$-0.6x=-\frac{140}{3}$$

Divide both sides by -0.6.

$$x=\frac{-\frac{140}{3}}{-0.6}$$

Express \frac{-\frac{140}{3}}{-0.6} as a single fraction.

$$x=\frac{-140}{3\left(-0.6\right)}$$

Multiply 3 and -0.6 to get -1.8.

$$x=\frac{-140}{-1.8}$$

Expand \frac{-140}{-1.8} by multiplying both numerator and the denominator by 10.

$$x=\frac{-1400}{-18}$$

Reduce the fraction \frac{-1400}{-18} to lowest terms by extracting and canceling out -2.

$$x=\frac{700}{9}$$