Solve 7[9-7(8-z)]-9=9[7(9z-8)+6]-82

$$7 [ 9 - 7 ( 8 - z ) ] - 9 = 9 [ 7 ( 9 z - 8 ) + 6 ] - 82$$

Solve for z

$$z=\frac{97}{259}\approx 0.374517375$$

Steps for Solving Linear Equation

Use the distributive property to multiply -7 by 8-z.

$$7\left(9-56+7z\right)-9=9\left(7\left(9z-8\right)+6\right)-82$$

Subtract 56 from 9 to get -47.

$$7\left(-47+7z\right)-9=9\left(7\left(9z-8\right)+6\right)-82$$

Use the distributive property to multiply 7 by -47+7z.

$$-329+49z-9=9\left(7\left(9z-8\right)+6\right)-82$$

Subtract 9 from -329 to get -338.

$$-338+49z=9\left(7\left(9z-8\right)+6\right)-82$$

Use the distributive property to multiply 7 by 9z-8.

$$-338+49z=9\left(63z-56+6\right)-82$$

Add -56 and 6 to get -50.

$$-338+49z=9\left(63z-50\right)-82$$

Use the distributive property to multiply 9 by 63z-50.

$$-338+49z=567z-450-82$$

Subtract 82 from -450 to get -532.

$$-338+49z=567z-532$$

Subtract 567z from both sides.

$$-338+49z-567z=-532$$

Combine 49z and -567z to get -518z.

$$-338-518z=-532$$

Add 338 to both sides.

$$-518z=-532+338$$

Add -532 and 338 to get -194.

$$-518z=-194$$

Divide both sides by -518.

$$z=\frac{-194}{-518}$$

Reduce the fraction \frac{-194}{-518} to lowest terms by extracting and canceling out -2.

$$z=\frac{97}{259}$$