solve and check 4(5z-5)-[2(3z-3)+1]

Question

4(5z-5)-[2(3z-3)+1].

Answer 1

The equation is 4(5z - 5) - [2(3z - 3) + 1] = 0.

Apply distributive property : a(b - c) = ab -ac.

4(5z) - 4(5) - 2(3z) + 2(3) - 1 = 0

20z - 20 - 6z + 6 - 1 = 0

Combine like terms.

Add 15 to each side.

14z - 15 +15 = 0 + 15

14z = 15

Divide each side by 14.

14z/14 = 15/14

z = 15/14.

CHECK :

To check the solution, substitute z = 15/14 in the original equation.

4[5(15/14) - 5] - [2{3(15/14) - 3} + 1] ≟ 0

4[(75 - 70)/14] - [2{45 - 42}/14 + 1] ≟ 0

4[5/14] - [6/14 + 1] ≟ 0

10/7 - [3/7 + 1] ≟ 0

10/7 - 10/7 ≟ 0

0 = 0.

The above stement is true, so z = 15/14 is the solution of the equation.