Solve x+43/57+x+46/54=x+49/51+x+52/48

$$\frac{ x+43 }{ 57 } + \frac{ x+46 }{ 54 } = \frac{ x+49 }{ 51 } + \frac{ x+52 }{ 48 }$$

Solve for x

$$x=-100$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 139536, the least common multiple of 57,54,51,48.

$$2448\left(x+43\right)+2584\left(x+46\right)=2736\left(x+49\right)+2907\left(x+52\right)$$

Use the distributive property to multiply 2448 by x+43.

$$2448x+105264+2584\left(x+46\right)=2736\left(x+49\right)+2907\left(x+52\right)$$

Use the distributive property to multiply 2584 by x+46.

$$2448x+105264+2584x+118864=2736\left(x+49\right)+2907\left(x+52\right)$$

Combine 2448x and 2584x to get 5032x.

$$5032x+105264+118864=2736\left(x+49\right)+2907\left(x+52\right)$$

Add 105264 and 118864 to get 224128.

$$5032x+224128=2736\left(x+49\right)+2907\left(x+52\right)$$

Use the distributive property to multiply 2736 by x+49.

$$5032x+224128=2736x+134064+2907\left(x+52\right)$$

Use the distributive property to multiply 2907 by x+52.

$$5032x+224128=2736x+134064+2907x+151164$$

Combine 2736x and 2907x to get 5643x.

$$5032x+224128=5643x+134064+151164$$

Add 134064 and 151164 to get 285228.

$$5032x+224128=5643x+285228$$

Subtract 5643x from both sides.

$$5032x+224128-5643x=285228$$

Combine 5032x and -5643x to get -611x.

$$-611x+224128=285228$$

Subtract 224128 from both sides.

$$-611x=285228-224128$$

Subtract 224128 from 285228 to get 61100.

$$-611x=61100$$

Divide both sides by -611.

$$x=\frac{61100}{-611}$$

Divide 61100 by -611 to get -100.

$$x=-100$$