Solve 45(8-x)+36=102-25(3x+24)

$$45 ( 8 - x ) + 36 = 102 - 25 ( 3 x + 24 )$$

Solve for x

$$x = -\frac{149}{5} = -29\frac{4}{5} = -29.8$$

Steps for Solving Linear Equation

Use the distributive property to multiply 45 by 8-x.

$$360-45x+36=102-25\left(3x+24\right)$$

Add 360 and 36 to get 396.

$$396-45x=102-25\left(3x+24\right)$$

Use the distributive property to multiply -25 by 3x+24.

$$396-45x=102-75x-600$$

Subtract 600 from 102 to get -498.

$$396-45x=-498-75x$$

Add 75x to both sides.

$$396-45x+75x=-498$$

Combine -45x and 75x to get 30x.

$$396+30x=-498$$

Subtract 396 from both sides.

$$30x=-498-396$$

Subtract 396 from -498 to get -894.

$$30x=-894$$

Divide both sides by 30.

$$x=\frac{-894}{30}$$

Reduce the fraction \frac{-894}{30} to lowest terms by extracting and canceling out 6.

$$x=-\frac{149}{5}$$