Question

Q.Solve and verify the following [email protected](2x+5)=3x-2

with the verification pls.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given linear equation is

$\rm :\longmapsto\:7x - (2x + 5) = 3x - 2$

Open the brackets and change the sign of inside, as outside there us negative sign.

So, we get

$\rm :\longmapsto\:7x - 2x - 5 = 3x - 2$

$\rm :\longmapsto\:5x - 5 = 3x - 2$

$\rm :\longmapsto\:5x - 3x = 5 - 2$

$\rm :\longmapsto\:2x = 3$

$\rm \implies\:\boxed{ \tt{ \: \: x \: = \: \frac{3}{2} \: \: }}$

Verification :-

Given linear equation is

$\rm :\longmapsto\:7x - (2x + 5) = 3x - 2$

Consider, LHS

$\rm :\longmapsto\:7x - (2x + 5)$

On substituting the value of x, we get

$\rm \:  =  \:7 \times \dfrac{3}{2} - \bigg[2 \times \dfrac{3}{2} + 5\bigg]$

$\rm \:  =  \: \dfrac{21}{2} - \bigg[3 + 5\bigg]$

$\rm \:  =  \: \dfrac{21}{2} -(8)$

$\rm \:  =  \: \dfrac{21}{2} - 8$

$\rm \:  =  \: \dfrac{21 - 16}{2}$

$\rm \:  =  \: \dfrac{5}{2}$

Now, Consider RHS

$\rm :\longmapsto\: 3x - 2$

On substituting the value of x, we get

$\rm \:  =  \:3 \times \dfrac{3}{2} - 2$

$\rm \:  =  \: \dfrac{9}{2} - 2$

$\rm \:  =  \: \dfrac{9 - 4}{2}$

$\rm \:  =  \: \dfrac{5}{2}$

Hence, LHS = RHS

Thus, Verified

Answer 2

$\huge\sf\underline\red{Solution}$

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$7x - (2x + 5) = 3x - 2 \\ \\ 7x - 2x - 5 = 3x - 2 \\ \\ 5x - 5 = 3x - 2 \\ \\ 5x - 3x = - 2 + 5 \\ \\ 2x = 3 \\ \\ x = \frac{3}{2}$

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$\huge\sf\underline\green{Verification}$

$7( \frac{3}{2} ) - (2 \times \frac{3}{2} + 5) = 3( \frac{3}{2} ) - 2 \\ \\ \frac{21}{2} - 8 = \frac{9}{2} - 2 \\ \\ \frac{21 - 16}{2} = \frac{9 - 4}{2} \\ \\ \frac{5}{2} = \frac{5}{2} \\ \\ \:LHS \: = \: \: RHS \: \: \\ \\ hence \: \: verified \:$

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