Question

Solve:

$\frac{12}{7} (x - 5) = 24 + 8x$
​

Answer 1

━━━━━━━━━━━━━━━━━━━━━━━━━

$\huge\purple{\mid{\fbox{\tt{ANSWER}}\mid}}$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\large \bold{\underline{\sf{\blue{We\:Have,}}}}$

$\frac{12}{7} (x - 5) = 24 + 8x$

Multiplying both sides by 7,we get

$7 \times \frac{12}{7} (x - 5) = 7 \times (24 + 8x) \\</em><em>$

$12(x - 5) = 7(24 + 8x) \\ </em><em>⇨</em><em>12x - 60 = 168 + 56x \\ </em>⇨<em>12x - 56x = 168 + 60 \\ </em><em>⇨</em><em> - 44x = 228 \\ </em><em>⇨</em><em> \frac{ - 44x}{ - 44} = \frac{228}{ - 44} \\ </em><em>⇨</em><em>x = \frac{ - 57}{11}$

$thus \: x = \frac{ - 57}{11} \: is \: the \: solution \: of \: the \: given \: equation.$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\large \bold{\underline{\sf{\blue{</em><em>Check</em><em>}}}}$

$substituting \: x = \frac{ - 57}{11} \: in \: the \: given \: equation \: we \: get \:$

$L.H.S = \frac{12}{7} (x - 5) \\ ⇨ \frac{12}{7} \times ( \frac{ - 57}{11} - 5) \\ ⇨ \frac{12}{7} \times ( \frac{ - 57 - 55}{11 } = \frac{12}{7} \times - \frac{112}{11} = 12 \times - \frac{16}{11} = - \frac{192}{11}$

And,

$</em><em>R.</em><em>H</em><em>.</em><em>S</em><em> \: = 24 + 8x \\</em>⇨<em> 24 + 8 \times - \frac{57}{11} = 24 - \frac{456}{11} = \frac{24 \times 11 - 456}{11} = \frac{264 - 456}{11} = - \frac{192}{11}$

$thus \: lhs = rhs \: for \: x = - \frac{57}{11}$

━━━━━━━━━━━━━━━━━━━━━━━━━

${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$

${\huge{\underline{\small{\mathbb{\pink{</p><p>~AngelicCandy♡ :)}}}}}}$

Answer 2

Question :-

• $\dfrac{12}{7} (x - 5) = 24 + 8x$

Solution :-

${⟼\: \dfrac{12}{7}\:(x-5)}$ $=$ $24+8x$

${⟼\: \dfrac{12x}{7}\:-\: \dfrac{60}{7}\:=\:24+8x}$

${⟼\: \dfrac{12x}{7}\:-\:8x\:=\:24+ \dfrac{60}{7}}$

${⟼\: \dfrac{12x-56x}{7}\:=\: \dfrac{168+60}{7}}$

${⟼\: \dfrac{-44x}{7}\:=\: \dfrac{228}{7}}$

${⟼\:-x\:=\: \dfrac{228}{7}\:×\: \dfrac{7}{49}}$

${⟼\:-x\:=\: \dfrac{57}{11}}$

${\boxed{\large{\bold{x\:=\: \dfrac{-57}{11}}}}}$