Solve 5[7-5(6-b)]-7=7[5(7b-6)+4]-50

$$5 [ 7 - 5 ( 6 - b ) ] - 7 = 7 [ 5 ( 7 b - 6 ) + 4 ] - 50$$

Solve for b

$$b=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5 by 6-b.

$$5\left(7-30+5b\right)-7=7\left(5\left(7b-6\right)+4\right)-50$$

Subtract 30 from 7 to get -23.

$$5\left(-23+5b\right)-7=7\left(5\left(7b-6\right)+4\right)-50$$

Use the distributive property to multiply 5 by -23+5b.

$$-115+25b-7=7\left(5\left(7b-6\right)+4\right)-50$$

Subtract 7 from -115 to get -122.

$$-122+25b=7\left(5\left(7b-6\right)+4\right)-50$$

Use the distributive property to multiply 5 by 7b-6.

$$-122+25b=7\left(35b-30+4\right)-50$$

Add -30 and 4 to get -26.

$$-122+25b=7\left(35b-26\right)-50$$

Use the distributive property to multiply 7 by 35b-26.

$$-122+25b=245b-182-50$$

Subtract 50 from -182 to get -232.

$$-122+25b=245b-232$$

Subtract 245b from both sides.

$$-122+25b-245b=-232$$

Combine 25b and -245b to get -220b.

$$-122-220b=-232$$

Add 122 to both sides.

$$-220b=-232+122$$

Add -232 and 122 to get -110.

$$-220b=-110$$

Divide both sides by -220.

$$b=\frac{-110}{-220}$$

Reduce the fraction \frac{-110}{-220} to lowest terms by extracting and canceling out -110.

$$b=\frac{1}{2}$$