Question

Solve and check by substitution.

pls see the question and solve...​

Answer 1

Given :

$\bigstar \; {\underline{\boxed{\tt{ \frac{7x + 3}{2} - \bigg( x - \frac{x - 2 }{3} \bigg) = 15}}}}$

To Find :

• The value of the variable x and the the solution

Solution:

By simplifying the term in the big brackets and making it non - complex .

${ : \implies } \sf \dfrac{7x + 3 }{2} - \bigg [ x - \dfrac{x - 2}{3} \bigg ] = 15 \\ \\ \\ \\ { : \implies } \sf \dfrac{7x + 3 }{2} - \bigg [\dfrac{3x}{3} - \dfrac{(x - 2)}{3} \bigg ] = 15 \\ \\ \\ \\ { : \implies } \sf \dfrac{7x + 3 }{2} - \bigg [ \dfrac{2x + 2}{3} \bigg ] = 15$

Multiplying the negative sign with the second fraction and simplifying it further we get the result

${ : \implies } \sf \dfrac{7x + 3 }{2} - \bigg [ \dfrac{2x + 2}{3} \bigg ] = 15 \\ \\ \\ \\ { : \implies } \sf \dfrac{7x + 3 }{2} - \dfrac{ 2x - 2}{3} = 15 \\ \\ \\ \\ { : \implies } \sf \dfrac{3 (7x + 3 ) }{2 \times 3 } - \dfrac{ 2 (2x - 2 )}{3 \times 2} = 15$

Simplifying the equation in further and transposing the terms we get ,

${ : \implies } \sf \dfrac{21x + 9 }{6} - \dfrac{ 4x - 4}{6} = 15 \\ \\ \\ \\ { : \implies } \sf \dfrac{21x + 9 - 4x - 4 }{6} = 15 \\ \\\\\\ { : \implies } \sf \dfrac{21x - 4x + 9 - 4}{6} = 15 \\ \\ \\ \\ { : \implies } \sf \dfrac{17x + 5 }{6} = 15 \\ \\ \\ \\ { : \implies } \sf 17x + 5 = 15 \times 6 \\ \\ \\ \\ { : \implies } \sf 17x + 5 = 90 \\ \\ \\ \\ { : \implies } \sf 17x =85 \\ \\ \\ \\ { : \implies } \sf x = \dfrac{85}{17} \\ \\ \\ \\ { : \implies}{\underline{\boxed{\sf{ x = 5 }}}\star}$

Verification :

$\rightarrow \bf \dfrac{7x + 3}{2} - \bigg( x - \dfrac{x - 2 }{3} \bigg) = 15$

$\rightarrow \bf \dfrac{7(5) + 3}{2} - \bigg( 5 - \dfrac{ (5 - 2 )}{3} \bigg) = 15$

$\rightarrow \bf \dfrac{35 + 3}{2} - \bigg( 5 - \dfrac{ (3 )}{3} \bigg) = 15$

$\rightarrow \bf \dfrac{38}{2} - \bigg( 5 - \dfrac{3}{3} \bigg) = 15$

$\rightarrow \bf \dfrac{38}{2} - \bigg( 5 - 1 \bigg) = 15$

$\rightarrow \bf 19- 4 = 15$

$\rightarrow \bf {\underline{\boxed{\bf 15 = 15 }}}$

• Hence verified.!!

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Step-by-step explanation:

7x+3−(x−3x−2)=15

\rightarrow \bf \dfrac{7(5) + 3}{2} - \bigg( 5 - \dfrac{ (5 - 2 )}{3} \bigg) = 15→27(5)+3−(5−3(5−2))=15

\rightarrow \bf \dfrac{35 + 3}{2} - \bigg( 5 - \dfrac{ (3 )}{3} \bigg) = 15→235+3−(5−3(3))=15

\rightarrow \bf \dfrac{38}{2} - \bigg( 5 - \dfrac{3}{3} \bigg) = 15→238−(5−33)=15

\rightarrow \bf \dfrac{38}{2} - \bigg( 5 - 1 \bigg) = 15→238−(5−1)=15

\rightarrow \bf 19- 4 = 15→19−4=15

\rightarrow \bf {\underline{\boxed{\bf 15 = 15 }}}→15=15