Solve 23x+17(40/23-17x/23)=80

$$23x+17( \frac{ 40 }{ 23 } - \frac{ 17x }{ 23 } )=80$$

Solve for x

$$x = \frac{29}{6} = 4\frac{5}{6} \approx 4.833333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 23.

$$529x+391\left(\frac{40}{23}-\frac{17x}{23}\right)=1840$$

Since \frac{40}{23} and \frac{17x}{23} have the same denominator, add them by adding their numerators.

$$529x+391\times \frac{40+17x}{23}=1840$$

Cancel out 23, the greatest common factor in 391 and 23.

$$529x+17\left(40+17x\right)=1840$$

Use the distributive property to multiply 17 by 40+17x.

$$529x+680+289x=1840$$

Combine 529x and 289x to get 818x.

$$818x+680=1840$$

Subtract 680 from both sides.

$$818x=1840-680$$

Subtract 680 from 1840 to get 1160.

$$818x=1160$$

Divide both sides by 818.

$$x=\frac{1160}{818}$$

Reduce the fraction \frac{1160}{818} to lowest terms by extracting and canceling out 2.

$$x=\frac{580}{409}$$