Solve the following equations1. \(\frac{2x}{x + 6} = 1\) 2. 10 = x +

1.	Solve the following equations1. \(\frac{2x}{x + 6} = 1\) 2. 10 = x + 33. 16 = 7x – 94. \(\frac{x + 5}x = 2 \frac{2}{3}\)
Answer» 1. \(\frac{2x}{x + 6} = 1\) By cross multiplication 2x = x + 6 ⇒ 2x – x = 6 \| On transposing x ⇒ x = 6 2. 10 = x + 3 ⇒ 10 – 3 = x \| On transposing 3 ⇒ 7 = x ⇒ x = 7 3. 16 = 7x – 9 ⇒ 16 + 9 = 7x \| On transposing – 9 ⇒ 25 = 7x ⇒ 7x = 25 ⇒ 7x/7 = 25/7 On dividing by 7 on both sides x = 25/7 4. \(\frac{x + 5}x = 2 \frac{2}{3}\) \(\frac{x + 5}x = \frac{8}{3}\) By cross multiplication ⇒ 3(x + 5) = 8x ⇒ 3x + 15 = 8x ⇒ 3x – 8x = – 15 On transposing 8x and 15 ⇒ – 5x = – 15 ⇒ -5x/-5 = -15/-5 \| On dividing by – 5 on both sides x = 3

Solve the following equations1. \(\frac{2x}{x + 6} = 1\) 2. 10 = x + 33. 16 = 7x – 94. \(\frac{x + 5}x = 2 \frac{2}{3}\)

Answer»

1. \(\frac{2x}{x + 6} = 1\)

By cross multiplication

2x = x + 6

⇒ 2x – x = 6 | On transposing x

⇒ x = 6

2. 10 = x + 3

⇒ 10 – 3 = x | On transposing 3

⇒ 7 = x

⇒ x = 7

3. 16 = 7x – 9

⇒ 16 + 9 = 7x | On transposing – 9

⇒ 25 = 7x

⇒ 7x = 25

⇒ 7x/7 = 25/7

On dividing by 7 on both sides

x = 25/7

4. \(\frac{x + 5}x = 2 \frac{2}{3}\)

\(\frac{x + 5}x = \frac{8}{3}\)

By cross multiplication

⇒ 3(x + 5) = 8x

⇒ 3x + 15 = 8x

⇒ 3x – 8x = – 15

On transposing 8x and 15

⇒ – 5x = – 15

⇒ -5x/-5 = -15/-5 | On dividing by – 5 on both sides

x = 3