Question

question is png please answer the questions​

Answer 1

Given:

1. $\dfrac{5x + 1}{3} = 7$

2. $\dfrac{5x}{3} + 3 = x + 7$

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What To Find:

We have to solve and check the equations.

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Solution 1:

$\dfrac{5x + 1}{3} = 7$

Use cross multiplication,

⇒ 5x + 1 = 7 × 3

Multiply 7 and 3,

⇒ 5x + 1 = 21

Take 1 to RHS,

⇒ 5x = 21 - 1

Subtract 1 from 21,

⇒ 5x = 20

Take 5 to RHS,

⇒ $x = \dfrac{20}{5}$

Divide 20 by 5,

⇒ x = 4

Checking 1:

$\dfrac{5x + 1}{3} = 7$

Subtitute the values,

⇒ $\dfrac{5 \times 4 + 1}{3} = 7$

Multiply and add the numerator,

⇒ $\dfrac{21}{3} = 7$

Divide 21 by 3,

⇒ 7 = 7

∴ LHS = RHS

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Solution 2:

$\dfrac{5x}{3} + 3 = x + 7$

Take 3 as 3/1,

⇒ $\dfrac{5x}{3} + \dfrac{3}{1} = x + 7$

LCM of 3 and 1 is 3,

⇒ $\dfrac{5x + 9}{3} = x + 7$

Take 3 to to LHS,

⇒ 5x + 9 = 3 (x + 7)

Multiply the brackets,

⇒ 5x + 9 = 3x + 21

Take 9 to RHS and 3x to LHS,

⇒ 5x - 3x = 21 - 9

Solve the bothe sides,

⇒ 2x = 12

Take 2 to RHS,

⇒ $x = \dfrac{12}{2}$

Divide 12 by 2,

⇒ x = 6

Checking 2:

$\dfrac{5x}{3} + 3 = x + 7$

Substitute the values,

⇒ $\dfrac{5 \times 6}{3} + 3 = 6 + 7$

Multiply the numerator,

⇒ $\dfrac{30}{3} + 3 = 6 + 7$

Cancel 30 by 3,

⇒ 10 + 3 = 6 + 7

Solve both sides,

⇒ 13 = 13

∴ LHS = RHS

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