Solve 3x+5/17+(11-x/76-3/4)=4+x/2-13

$$\frac { 3 x + 5 } { 17 } + ( \frac { 11 - x } { 76 } - \frac { 3 } { 4 } ) = \frac { 4 + x } { 2 } - 13$$

Solve for x

$$x = \frac{2762}{87} = 31\frac{65}{87} \approx 31.747126437$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 1292, the least common multiple of 17,76,4,2.

$$76\left(3x+5\right)+17\left(11-x\right)-969=646\left(4+x\right)-16796$$

Use the distributive property to multiply 76 by 3x+5.

$$228x+380+17\left(11-x\right)-969=646\left(4+x\right)-16796$$

Use the distributive property to multiply 17 by 11-x.

$$228x+380+187-17x-969=646\left(4+x\right)-16796$$

Add 380 and 187 to get 567.

$$228x+567-17x-969=646\left(4+x\right)-16796$$

Combine 228x and -17x to get 211x.

$$211x+567-969=646\left(4+x\right)-16796$$

Subtract 969 from 567 to get -402.

$$211x-402=646\left(4+x\right)-16796$$

Use the distributive property to multiply 646 by 4+x.

$$211x-402=2584+646x-16796$$

Subtract 16796 from 2584 to get -14212.

$$211x-402=-14212+646x$$

Subtract 646x from both sides.

$$211x-402-646x=-14212$$

Combine 211x and -646x to get -435x.

$$-435x-402=-14212$$

Add 402 to both sides.

$$-435x=-14212+402$$

Add -14212 and 402 to get -13810.

$$-435x=-13810$$

Divide both sides by -435.

$$x=\frac{-13810}{-435}$$

Reduce the fraction \frac{-13810}{-435} to lowest terms by extracting and canceling out -5.

$$x=\frac{2762}{87}$$