Question
$\frac{6\text{x}-2}{9}+\frac{3\text{x}+5}{18}=\frac13$
✓
Answer
$\frac{6\text{x}-2}{9}+\frac{3\text{x+5}}{18}=\frac13$
$=\frac{6\text{x}(2)-2(2)+\text{3x}+5}{18}=\frac13$
$=\frac{12\text{x}-4+3\text{x}+5}{18}=\frac13$
$=\frac{15\text{x}+1}{18}=\frac13$ Multiplying both sides by $18$, we get
$=\frac{15\text{x}+1}{18}\times18=\frac12\times18$
$=15\text{x}+1=6$ Transposing $1$ to
$R.H.S$., we get $= 15x = 6 - 1 = 15x = 5$
Dividing both sides by $15$, we get
$=\frac{15\text{x}}{15}=\frac{5}{15}$
$=\text{x}=\frac13$ Verification: Substituting $\text{x}=\frac13$ both sides,
we get $\frac{6\big(\frac13\big)-2}{9}+\frac{3\big(\frac13\big)+5}{18}=\frac13$
$\frac{2-2}{9}+\frac{1+5}{18}=\frac13$
$0+\frac{6}{18}=\frac13$
$\frac13=\frac13$
$L.H.S. = R.H.S.$
Hence, verified.
$=\frac{6\text{x}(2)-2(2)+\text{3x}+5}{18}=\frac13$
$=\frac{12\text{x}-4+3\text{x}+5}{18}=\frac13$
$=\frac{15\text{x}+1}{18}=\frac13$ Multiplying both sides by $18$, we get
$=\frac{15\text{x}+1}{18}\times18=\frac12\times18$
$=15\text{x}+1=6$ Transposing $1$ to
$R.H.S$., we get $= 15x = 6 - 1 = 15x = 5$
Dividing both sides by $15$, we get
$=\frac{15\text{x}}{15}=\frac{5}{15}$
$=\text{x}=\frac13$ Verification: Substituting $\text{x}=\frac13$ both sides,
we get $\frac{6\big(\frac13\big)-2}{9}+\frac{3\big(\frac13\big)+5}{18}=\frac13$
$\frac{2-2}{9}+\frac{1+5}{18}=\frac13$
$0+\frac{6}{18}=\frac13$
$\frac13=\frac13$
$L.H.S. = R.H.S.$
Hence, verified.
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