Question

Solve 2/3 + 5a = 4 in 2 methods

Answer 1

Given:

• To solve ⅔ + 5a = 4

Solving by using Method I:

$\sf{ \dfrac{ 2}{ 3} + 5a = 4 }$

• Multiplying each term by 3

$\implies \sf{3 \times \dfrac{2}{3} + 3 \times 5a = 4 \times 3 }$

$\implies \sf{ 2 + 15a = 12 }$

$\implies \sf{ 15a = 12 - 2 }$

$\implies \sf{15a = 10}$

$\implies \sf{a = \dfrac{\cancel{10}}{\cancel{15}}}$

   

$\therefore \; \boxed{\sf{\orange{ a = \dfrac{2}{3} }}}$

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Solving by using Method II:

$\sf{ \dfrac{ 2}{ 3} + 5a = 4 }$

• Subtracting ⅔ from both the sides

$\implies \sf{ \dfrac{2}{3} + 5a - \dfrac{2}{3} = 4 - \dfrac{2}{3} }$

$\implies \sf{ 5a = \dfrac{12-2}{3} }$

$\implies \sf{ 5a = \dfrac{10}{3} }$

• Dividing both sides by 5

$\implies \sf{ \dfrac{5a}{5} = \dfrac{10}{3} \times \dfrac{1}{5} }$

     

$\therefore \; \boxed{\orange{\sf{a = \dfrac{2}{3}}}}$

   

─ Therefore, we got the common answer by trying out the two different methods. We get the conclusion as a = ⅔.

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Answer 2

Given:

• To solve ⅔ + 5a = 4

Solving by using Method I:

$\sf{ \dfrac{ 2}{ 3} + 5a = 4 }$

• Multiplying each term by 3

$\implies \sf{3 \times \dfrac{2}{3} + 3 \times 5a = 4 \times 3 }$

$\implies \sf{ 2 + 15a = 12 }$

$\implies \sf{ 15a = 12 - 2 }$

$\implies \sf{15a = 10}$

$\implies \sf{a = \dfrac{\cancel{10}}{\cancel{15}}}$

   

$\therefore \; \boxed{\sf{\orange{ a = \dfrac{2}{3} }}}$

___

Solving by using Method II:

$\sf{ \dfrac{ 2}{ 3} + 5a = 4 }$

• Subtracting ⅔ from both the sides

$\implies \sf{ \dfrac{2}{3} + 5a - \dfrac{2}{3} = 4 - \dfrac{2}{3} }$

$\implies \sf{ 5a = \dfrac{12-2}{3} }$

$\implies \sf{ 5a = \dfrac{10}{3} }$

• Dividing both sides by 5

$\implies \sf{ \dfrac{5a}{5} = \dfrac{10}{3} \times \dfrac{1}{5} }$

     

$\therefore \; \boxed{\orange{\sf{a = \dfrac{2}{3}}}}$

   

─ Therefore, we got the common answer by trying out the two different methods. We get the conclusion as a = ⅔.

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