$\"\"$

The equation is 4z + b = 2z + c.

According to subtraction property of equality; if a = b than a $\"\"$ c = b $\"\"$ c.

4z + b $\"\"$ 2z = 2z + c $\"\"$ 2z (Subtract 2z from each side)

4z $\"\"$ 2z + b = c (Additive inverse property:2z $\"\"$ 2z = 0)

2z + b = c (Subtract: 4z $\"\"$ 2z = 2z)

2z + b $\"\"$ b = c $\"\"$ b (Subtract b from each side)

2z = c $\"\"$ b (Additive inverse property: b $\"\"$ b = 0)

$\"\"$

$\"\"$ (Divide each side by 2)

$\"\"$ (Cancel common terms) $\"\"$

Verify:

To check the solution, substitute $\"\"$ in original equation. \ \

$\"\"$

$\"\"$ (Cancel common terms)

$\"\"$ (Divide: $\"\"$ )

$\"\"$ (Distributive property: a(b $\"\"$ c) = ab $\"\"$ ac)

Compare the values, the equation is true.

$\"\"$

The value of z is $\"\"$ .