Solve 7/x+3/5=-1/10

$$\frac { 7 } { x } + \frac { 3 } { 5 } = \frac { - 1 } { 10 }$$

Solve for x

$$x=-10$$

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 10x, the least common multiple of x,5,10.

$$10\times 7+10x\times \frac{3}{5}=x\left(-1\right)$$

Multiply 10 and 7 to get 70.

$$70+10x\times \frac{3}{5}=x\left(-1\right)$$

Express 10\times \frac{3}{5} as a single fraction.

$$70+\frac{10\times 3}{5}x=x\left(-1\right)$$

Multiply 10 and 3 to get 30.

$$70+\frac{30}{5}x=x\left(-1\right)$$

Divide 30 by 5 to get 6.

$$70+6x=x\left(-1\right)$$

Subtract x\left(-1\right) from both sides.

$$70+6x-x\left(-1\right)=0$$

Combine 6x and -x\left(-1\right) to get 7x.

$$70+7x=0$$

Subtract 70 from both sides. Anything subtracted from zero gives its negation.

$$7x=-70$$

Divide both sides by 7.

$$x=\frac{-70}{7}$$

Divide -70 by 7 to get -10.

$$x=-10$$