Question

(b). Solve for x and verify the result: 5x + 3 = 4/3 (1+x)​

Answer 1

`x = - (5)/(11) \\`

Explanation:

`5x + 3 = (4)/(3) (1 + x) \\ 5x + 3 = (4)/(3) + (4x)/(3) \\ 5x - (4x)/(3) = (4)/(3) - 3 \\ (3(5x) - 4x)/(3) = (4 - 3(3))/(3) \\ (15x - 4x)/(3) = (4 - 9)/(3) \\ (11x)/(3) = - (5)/(3) \\ 11x = - (5)/(3) * 3 \\ 11x = - 5 \\ x = - (5)/(11) \\`

Answer 2

`{\dashrightarrow\sf{5x + 3 = (4)/(3) \bigg(1 + x \bigg)}}`

`{\dashrightarrow\sf{3 \bigg(5x + 3 \bigg)= 4\bigg(1 + x \bigg)}}`

`{\dashrightarrow\sf{\bigg(5x * 3 + 3 * 3 \bigg)= \bigg(1 * 4 + x * 4 \bigg)}}`

`{\dashrightarrow\sf{\bigg(15x + 9 \bigg)= \bigg(4 + 4x\bigg)}}`

`{\dashrightarrow\sf{15x - 4x =4 - 9 }}`

`{\dashrightarrow\sf{11x =4 - 9 }}`

`{\dashrightarrow\sf{11x = - 5 }}`

`{\dashrightarrow\sf{x = - (5)/(11)}}`

`\bigstar{\underline{\boxed{\sf{\red{x = - (5)/(11)}}}}}`

∴ The value of x is -5/11.

`\begin{gathered}\end{gathered}`

Verification :

`{\dashrightarrow\sf{5x + 3 = (4)/(3) \bigg(1 + x \bigg)}}`

`{\dashrightarrow\sf{ \bigg(\left\{5 * - (5)/(11) \right\} + 3 \bigg)= (4)/(3) \bigg(1 + \left\{ - (5)/(10)\right\}\bigg)}}`

`{\dashrightarrow\sf{ \bigg(\left\{- (25)/(11) \right\} + 3 \bigg)= (4)/(3) \bigg(1 + \left\{ - (5)/(11)\right\}\bigg)}}`

`{\dashrightarrow\sf{ \bigg( ( - ( 25 )+ (3 * 11))/(11) \bigg)= (4)/(3) \bigg( ((1 * 11) - (5 * 1))/(11)\bigg)}}`

`{\dashrightarrow\sf{ \bigg( ( - 25+ 33)/(11) \bigg)= (4)/(3) \bigg( (11 - 5)/(11)\bigg)}}`

`{\dashrightarrow\sf{ \bigg( (8)/(11) \bigg)= (4)/(3) \bigg( (6)/(11)\bigg)}}`

`{\dashrightarrow\sf{ \bigg( (8)/(11) \bigg)= \bigg((4)/(3) * (6)/(11)\bigg)}}`

`{\dashrightarrow\sf{ \bigg( (8)/(11) \bigg)= \bigg((4 * 6)/(3 * 11)\bigg)}}`

`{\dashrightarrow\sf{ \bigg( (8)/(11) \bigg)= \bigg((24)/(33)\bigg)}}`

`{\dashrightarrow\sf{ \bigg( (8)/(11) \bigg)= \bigg(\cancel{(24)/(33)}\bigg)}}`

`{\dashrightarrow\sf{ \bigg( (8)/(11) \bigg)= \bigg({(8)/(11)}\bigg)}}`

`\bigstar{\underline{\boxed{\sf{\red{LHS = RHS}}}}}`

∴ Hence Verified !