Solve the following equations:1. 15(x – 1) + 4(x + 3) = 2 (7 + x) 2

1.	Solve the following equations:1. 15(x – 1) + 4(x + 3) = 2 (7 + x) 2. 3 (5z – 7) +2 (9z – 11) = 4 (8z – 7) – 111 3. 8(x – 3) – (6 – 2x) = 2(x + 2) – 5 (5 – x) 4. 3(n – 4)+2(4n – 5) = 5(n + 2) + 16
Answer» 1. 15(x – 1) + 4(x + 3) = 2(7 + x) ⇒ 15x – 15 + 4x + 12= 14 + 2x ⇒ 19x – 3 = 14 + 2x ⇒ 19x – 2x = 14 + 3 ⇒ 17x = 17 x = \(\frac{17}{17}\) = 1 ∴ x = 1 2. 3(5z – 7) + 2(9z – 11) = 4(8z – 7) – 111 ⇒ 15z – 21 + 18z – 22 = 32z – 28 – 111 ⇒ 33z – 43 = 32z – 139 ⇒ 33z – 32z = – 139 + 43 ∴ z = – 96 3. 8(x – 3) – (6 – 2x) = 2(x + 2) - 5(5 – x) ⇒ 8x – 24 – 6 + 2x = 2x + 4 – 25 + 5x ⇒ 8x – 30 = 5x – 21 ⇒ 8x – 5x= –21 + 30 ⇒ 3x = 9 ∴ x = 3 4. 3(n – 4) + 2(4n – 5) = 5(n + 2) + 16 ⇒ 3n – 12 + 8n – 10 = 5n + 10 + 16 ⇒ 11n – 22 = 5n + 26 ⇒ 11n – 5n = 26 + 22 ⇒ 6n =48 ⇒ n = \(\frac{48}6\) = 8 ∴ n = 8

Solve the following equations:1. 15(x – 1) + 4(x + 3) = 2 (7 + x) 2. 3 (5z – 7) +2 (9z – 11) = 4 (8z – 7) – 111 3. 8(x – 3) – (6 – 2x) = 2(x + 2) – 5 (5 – x) 4. 3(n – 4)+2(4n – 5) = 5(n + 2) + 16

Answer»

1. 15(x – 1) + 4(x + 3) = 2(7 + x)

⇒ 15x – 15 + 4x + 12= 14 + 2x

⇒ 19x – 3 = 14 + 2x

⇒ 19x – 2x = 14 + 3

⇒ 17x = 17

x = \(\frac{17}{17}\) = 1

∴ x = 1

2. 3(5z – 7) + 2(9z – 11) = 4(8z – 7) – 111

⇒ 15z – 21 + 18z – 22 = 32z – 28 – 111

⇒ 33z – 43 = 32z – 139

⇒ 33z – 32z = – 139 + 43

∴ z = – 96

3. 8(x – 3) – (6 – 2x) = 2(x + 2) - 5(5 – x)

⇒ 8x – 24 – 6 + 2x = 2x + 4 – 25 + 5x

⇒ 8x – 30 = 5x – 21

⇒ 8x – 5x= –21 + 30

⇒ 3x = 9

∴ x = 3

4. 3(n – 4) + 2(4n – 5) = 5(n + 2) + 16

⇒ 3n – 12 + 8n – 10 = 5n + 10 + 16

⇒ 11n – 22 = 5n + 26

⇒ 11n – 5n = 26 + 22

⇒ 6n =48

⇒ n = \(\frac{48}6\) = 8

∴ n = 8