Solve 82=14+25(x-3)+38(x+8)

$$82 = 14 + 25 ( x - 3 ) + 38 ( x + 8 )$$

Solve for x

$$x = -\frac{23}{9} = -2\frac{5}{9} \approx -2.555555556$$

Steps for Solving Linear Equation

Use the distributive property to multiply 25 by x-3.

$$82=14+25x-75+38\left(x+8\right)$$

Subtract 75 from 14 to get -61.

$$82=-61+25x+38\left(x+8\right)$$

Use the distributive property to multiply 38 by x+8.

$$82=-61+25x+38x+304$$

Combine 25x and 38x to get 63x.

$$82=-61+63x+304$$

Add -61 and 304 to get 243.

$$82=243+63x$$

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

$$243+63x=82$$

Subtract 243 from both sides.

$$63x=82-243$$

Subtract 243 from 82 to get -161.

$$63x=-161$$

Divide both sides by 63.

$$x=\frac{-161}{63}$$

Reduce the fraction \frac{-161}{63} to lowest terms by extracting and canceling out 7.

$$x=-\frac{23}{9}$$