Solve 62/3divx-8=-425/7-3

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

Solve for x

$$x=-\frac{35}{198}\approx -0.176767677$$

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.

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

Multiply 6 and 3 to get 18.

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

Add 18 and 2 to get 20.

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

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

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

Multiply 7 and 20 to get 140.

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

Multiply 7 and -8 to get -56.

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

Multiply 42 and 7 to get 294.

$$\frac{140}{3}-56x=-x\left(294+5\right)+7x\left(-3\right)$$

Add 294 and 5 to get 299.

$$\frac{140}{3}-56x=-x\times 299+7x\left(-3\right)$$

Multiply 7 and -3 to get -21.

$$\frac{140}{3}-56x=-x\times 299-21x$$

Add x\times 299 to both sides.

$$\frac{140}{3}-56x+x\times 299=-21x$$

Combine -56x and x\times 299 to get 243x.

$$\frac{140}{3}+243x=-21x$$

Add 21x to both sides.

$$\frac{140}{3}+243x+21x=0$$

Combine 243x and 21x to get 264x.

$$\frac{140}{3}+264x=0$$

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

$$264x=-\frac{140}{3}$$

Divide both sides by 264.

$$x=\frac{-\frac{140}{3}}{264}$$

Express \frac{-\frac{140}{3}}{264} as a single fraction.

$$x=\frac{-140}{3\times 264}$$

Multiply 3 and 264 to get 792.

$$x=\frac{-140}{792}$$

Reduce the fraction \frac{-140}{792} to lowest terms by extracting and canceling out 4.

$$x=-\frac{35}{198}$$