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Solving Equations with Variables on Both Sides

x = 4/5 x + 1...

Question

$x = \frac{4}{5} (x + 10)$
$x = 50$
If this is true enter 1, if false enter 0.

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Solution

$G i v e n, x = \frac{4}{5} (x + 10) \Rightarrow 5 x = 4 (x + 10) [O n c r o s s - m u l t i p l i c a t i o n] \Rightarrow 5 x = 4 x + 40 \Rightarrow 5 x - 4 x = 40 [T r a n s p o s i n g 4 x t o L H S] \Rightarrow x = 40$

Check:
LHS = x=40
$R H S = \frac{4}{5} (x + 10) = \frac{4}{5} (40 + 10) = \frac{4}{5} \times 50 = 4 \times 10 = 40$
Clearly, LHS = RHS
Hence checked!!

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