Question

Q23. Solve equations and check your answers.
13(y-4)-3(y-9) = 5(y+4)​

Answer 1

Answer :-

$\sf Q) \: 13 \:(y - 4) - 3 \: (y - 9) = 5 \: (y + 4)$

Removing the brackets, multiplying the numbers outside the brackets by the numbers inside the brackets,

$\Rightarrow\sf13y - 52 - 3y + 27 = 5y + 20$

Keeping the constant and variable terms separately,

$\Rightarrow \sf13y - 3y - 52 + 27 = 5y + 20$

On simplifying,

$\Rightarrow\sf10y - 25 = 5y + 20$

Transposing 5y from RHS to LHS, changing it's sign,

$\Rightarrow\sf10y - 5y - 25 = 20$

On simplifying,

$\Rightarrow\sf5y - 25 = 20$

Transposing 25 from LHS to RHS, changing it's sign,

$\Rightarrow\sf5y = 20 + 25$

On simplifying,

$\Rightarrow\sf5y = 45$

Transposing 5 from LHS to RHS, changing it's sign,

$\Rightarrow\sf y = \dfrac{45}{5}$

Dividing 45 by 5,

$\Rightarrow \sf y =9.$

• The value of y is 9.

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Verification :-

To check our answer, let's put 9 (The value of y) in place of y and see whether LHS = RHS.

$\underline{\underline{\mathfrak{Substituting \: the \: value \: of \: y,}}}$

LHS

$\implies\rm13 \: (9 - 4) - 3\: (9 - 9)$

Simplifying the numbers inside the brackets,

$\implies \rm13 \: (5) - 3 \: (0)$

Removing the brackets,

$\implies \rm13 \times 5 - 3 \times 0$

On multiplying the numbers,

$\implies\rm65 - 0$

On simplifying,

$\implies \rm65.$

RHS

$\implies \rm5 \: (9 + 4)$

Simplifying the numbers inside the brackets,

$\rm\implies 5 \: (13)$

Removing the brackets,

$\rm\implies 5 \times 13$

On multiplying the numbers,

$\rm \implies 65.$

Since LHS = RHS,

Hence verified!

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