Question

solve the equation and verify your answer 2x\5-3\2=x\2+1​

Answer 1

$\frac{2x}{5} - \frac{3}{2} = \frac{x}{2} + 1 \\ \frac{2 \times (2x) - 5 \times 3}{10} = \frac{x + 2 \times 1}{2} \\ \frac{4x - 15}{10} = \frac{x + 2}{2} \\ (4x - 15) \times 2 = (x + 2) \times 10 \\ 8x - 30 = 10x + 20 \\ 8x - 10x = 20 + 30 \\ - 2x = 50 \\ x = \frac{50}{ - 2} \\ x = \frac{ - 50}{2} \\ x = - 25$

-25 is the value of x.

Now we'll do verification method.

$\frac{2x}{5} - \frac{3}{2} = \frac{x}{2} + 1 \\ \frac{2 \times ( - 25)}{5} - \frac{3}{2} = \frac{ - 25}{2} + 1 \\ \frac{ - 50}{5} - \frac{3}{2} = \frac{ - 25}{2} + 1 \\ - 10 - \frac{3}{2} = \frac{ - 25}{2} + 1 \\ \frac{ - 10 \times 2 - 3}{2} = \frac{ - 25 + 1 \times 2}{2} \\ \frac{ - 20 - 3}{2} = \frac{ - 25 + 2}{2} \\ \frac{ - 23}{2} = \frac{ - 23}{2}$

So, LHS = RHS

Hence proved.

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