Question

solve for x x+4/4+x-5/3=11​

Answer 1

Step-by-step explanation:

$\dashrightarrow \sf \dfrac{x + 4}{4} + \dfrac{x - 5}{3} = 11$

$\sf LCM \:of \: 4 \: and \: 3 \: is \: 12$

$\dashrightarrow \sf \dfrac{3(x + 4) + 4(x - 5)}{12} = 11$

$\dashrightarrow \sf \dfrac{3x + 12 + 4x - 20}{12} = 11$

$\dashrightarrow \sf \dfrac{3x + 4x + 12- 20}{12} = 11$

$\dashrightarrow \sf \dfrac{7x - 8}{12} = 11$

$\dashrightarrow \sf 7x - 8 = 11 \times 12$

$\dashrightarrow \sf 7x - 8 =132$

$\dashrightarrow \sf 7x =132 + 8$

$\dashrightarrow \sf 7x =140$

$\dashrightarrow \sf x = \dfrac{140}{7} = 20$

$\dashrightarrow \underline{\boxed{\sf x = 20}}$

$\sf \underline{Let's check }$

$\dashrightarrow \sf \dfrac{x + 4}{4} + \dfrac{x - 5}{3} = 11$

$\sf Substitute \: x = 20 \: in \: the \: equation$

$\dashrightarrow \sf \dfrac{20 + 4}{4} + \dfrac{20 - 5}{3} = 11$

$\dashrightarrow \sf \dfrac{24}{4} + \dfrac{15}{3} = 11$

$\dashrightarrow \sf 6 + 5 = 11$

$\dashrightarrow \sf 11 = 11$

$\sf LHS = RHS$

$\sf Hence,\: verified$