Solve x+1/58+x+2/57=x+3/56+x+4/55

$$\frac { x + 1 } { 58 } + \frac { x + 2 } { 57 } = \frac { x + 3 } { 56 } + \frac { x + 4 } { 55 }$$

Solve for x

$$x=-59$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5091240, the least common multiple of 58,57,56,55.

$$87780\left(x+1\right)+89320\left(x+2\right)=90915\left(x+3\right)+92568\left(x+4\right)$$

Use the distributive property to multiply 87780 by x+1.

$$87780x+87780+89320\left(x+2\right)=90915\left(x+3\right)+92568\left(x+4\right)$$

Use the distributive property to multiply 89320 by x+2.

$$87780x+87780+89320x+178640=90915\left(x+3\right)+92568\left(x+4\right)$$

Combine 87780x and 89320x to get 177100x.

$$177100x+87780+178640=90915\left(x+3\right)+92568\left(x+4\right)$$

Add 87780 and 178640 to get 266420.

$$177100x+266420=90915\left(x+3\right)+92568\left(x+4\right)$$

Use the distributive property to multiply 90915 by x+3.

$$177100x+266420=90915x+272745+92568\left(x+4\right)$$

Use the distributive property to multiply 92568 by x+4.

$$177100x+266420=90915x+272745+92568x+370272$$

Combine 90915x and 92568x to get 183483x.

$$177100x+266420=183483x+272745+370272$$

Add 272745 and 370272 to get 643017.

$$177100x+266420=183483x+643017$$

Subtract 183483x from both sides.

$$177100x+266420-183483x=643017$$

Combine 177100x and -183483x to get -6383x.

$$-6383x+266420=643017$$

Subtract 266420 from both sides.

$$-6383x=643017-266420$$

Subtract 266420 from 643017 to get 376597.

$$-6383x=376597$$

Divide both sides by -6383.

$$x=\frac{376597}{-6383}$$

Divide 376597 by -6383 to get -59.

$$x=-59$$