Solve 1/5x-13/10x=7/2x-23/10..7

$$\frac { 1 } { 5 x } - \frac { 13 } { 10 x } = \frac { 7 } { 2 x } - 2 \frac { 3 } { 10 } . .7$$

Solve for x

$$x=2$$

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 5x,10x,2x,10.

$$2-13=5\times 7-x\left(2\times 10+3\right)$$

Subtract 13 from 2 to get -11.

$$-11=5\times 7-x\left(2\times 10+3\right)$$

Multiply 5 and 7 to get 35.

$$-11=35-x\left(2\times 10+3\right)$$

Multiply 2 and 10 to get 20.

$$-11=35-x\left(20+3\right)$$

Add 20 and 3 to get 23.

$$-11=35-x\times 23$$

Swap sides so that all variable terms are on the left hand side.

$$35-x\times 23=-11$$

Subtract 35 from both sides.

$$-x\times 23=-11-35$$

Subtract 35 from -11 to get -46.

$$-x\times 23=-46$$

Divide both sides by -1.

$$x\times 23=\frac{-46}{-1}$$

Fraction \frac{-46}{-1} can be simplified to 46 by removing the negative sign from both the numerator and the denominator.

$$x\times 23=46$$

Divide both sides by 23.

$$x=\frac{46}{23}$$

Divide 46 by 23 to get 2.

$$x=2$$