Solve the equation
6(z – 2)   = 3z – 8 +3z 
6z - 12 = 6z - 8 {distributive property and combined like terms}
6z = 6z + 4 {added 12 to both sides}
0 = 4 {subtracted 6z from both sides}
= no solution 

When the variable disappears and you get a statement that is
never true, then there is "no solution" 

© Algebra House

---

Solve the equation
5(2n - 2) = 20
5(2n) - 5(2) = 20 {used distributive property with 5}
10n - 10 = 20 {multiplied -5 by 2}
10n = 30 {added 10 to both sides}
n = 3 {divided both sides by 10} 

© Algebra House

---

Solve the rational equation

(x - 1)
--------- = 2/5 
(x + 9) 

5(x - 1) = 2(x + 9) {cross-multiplied}
5x - 5 = 2x + 18 {used distributive property}
5x = 2x + 23 {added 5 to both sides}
3x = 23 {subtracted 2x from both sides}
x = 23/3 {divided both sides by 3}

© Algebra House

Solve the equation
13 + 4w = -5(-w – 6) + 2(w + 1)
13 + 4w = 5w + 30 + 2w + 2 {used distributive property}
13 + 4w = 7w + 32 {combined like terms}
4w = 7w + 19 {subtracted 13 from both sides}
-3w = 19 {subtracted 7w from both sides}
w = -19/3 {divided both sides by -3}

© Algebra House

---

Solve the equation for x.
2[9 - (x - 3) + 4x] = 4x - 5(x + 2) – 8
2[9 - x + 3 + 4x] = 4x - 5x - 10 - 8 {used distributive property} 
2[3x + 12] = -x - 18 {combined like terms}
6x + 24 = -x - 18 {used distributive property}
7x + 24 = -18 {added x to both sides}
7x = - 42 {subtracted 24 from both sides}
x = - 6 {divided both sides by 7} 

© Algebra House