Solve (xdiv8+1)*2-8=(xdiv9+1)*2+8

$$( x \div 8 + 1 ) \times 2 - 8 = ( x \div 9 + 1 ) \times 2 + 8$$

Solve for x

$$x=576$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 72, the least common multiple of 8,9.

$$72\left(\frac{x}{8}+1\right)\times 2-576=72\left(\frac{x}{9}+1\right)\times 2+576$$

Multiply 72 and 2 to get 144.

$$144\left(\frac{x}{8}+1\right)-576=72\left(\frac{x}{9}+1\right)\times 2+576$$

Use the distributive property to multiply 144 by \frac{x}{8}+1.

$$144\times \frac{x}{8}+144-576=72\left(\frac{x}{9}+1\right)\times 2+576$$

Cancel out 8, the greatest common factor in 144 and 8.

$$18x+144-576=72\left(\frac{x}{9}+1\right)\times 2+576$$

Subtract 576 from 144 to get -432.

$$18x-432=72\left(\frac{x}{9}+1\right)\times 2+576$$

Multiply 72 and 2 to get 144.

$$18x-432=144\left(\frac{x}{9}+1\right)+576$$

Use the distributive property to multiply 144 by \frac{x}{9}+1.

$$18x-432=144\times \frac{x}{9}+144+576$$

Cancel out 9, the greatest common factor in 144 and 9.

$$18x-432=16x+144+576$$

Add 144 and 576 to get 720.

$$18x-432=16x+720$$

Subtract 16x from both sides.

$$18x-432-16x=720$$

Combine 18x and -16x to get 2x.

$$2x-432=720$$

Add 432 to both sides.

$$2x=720+432$$

Add 720 and 432 to get 1152.

$$2x=1152$$

Divide both sides by 2.

$$x=\frac{1152}{2}$$

Divide 1152 by 2 to get 576.

$$x=576$$