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in Linear Equations with One Variable by (48.4k points)
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Solve the following equations

1. \(\frac{2x}{x + 6} = 1\) 

2. 10 = x + 3

3. 16 = 7x – 9

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

1 Answer

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Best 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

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