Question

Solve and check result: \(\frac{2x}{3}+1 =\frac{ 7x}{15}+3\)

Answer 1

\(\frac{2x}{3}+1 =\frac{ 7x}{15}+3\)

Transposing \(\frac{7x}{15}\) to L.H.S and \(1\) to R.H.S, we obtain

\(\frac{2x}{3}-\frac{7x}{15}\) = \(3-1\)

\(\frac{5 × 2x - 7x }{ 15}\) = 2

\(\frac{3x}{15} = 2\)

\(\frac{x}{5}\) = 2
Multiplying both sides by \(5\), we obtain
\(x = 10\)
L.H.S = \(\frac{2x}{3}+1\) 

= \(\frac{2×10}{3}+1\)

= \(\frac{2 ×10+1×3}{3}\) 

= \(\frac{23}{3}\)

R.H.S = \(\frac{7x}{15}+3\)

=\(\frac{7×10}{15}+3\) 

= \(\frac{7 × 2}{3}+3\) 

= \(\frac{14}{3}+3\) 

= \(\frac{14+3 × 3}{3}\) 

= \(\frac{23}{3}\)

L.H.S. = R.H.S. 

Hence, the result obtained above is correct