Question
Solve the following equations. Check your result in case. $\frac{\text{y}-1}{3}-\frac{\text{y}-2}{4}=1$
✓
Answer
$\frac{\text{y}-1}{3}-\frac{\text{y}-2}{4}=1$
$\frac{4(\text{y}-1)-3(\text{y}-2)}{12}=1$ (LCM of $3, 4 = 12)$
$\Rightarrow\frac{4\text{y}-4-3\text{y}+6}{12}=1$
$\Rightarrow\frac{\text{y}+2}{12}=1$
$\Rightarrow\text{y}+2=12$
$\Rightarrow\text{y}=12-2=10$
$\Rightarrow\text{y}=10$
Check: $\text{L.H.S.}=\frac{\text{y}-1}{3}-\frac{\text{y}-2}{4}$
$=\frac{10-1}{3}-\frac{10-2}{4}$
$=\frac{9}{3}-\frac{8}{4}=3-2$
$=1$
$=\text{R.H.S. = L.H.S.}$ Hence $= \text{y}=10$
$\frac{4(\text{y}-1)-3(\text{y}-2)}{12}=1$ (LCM of $3, 4 = 12)$
$\Rightarrow\frac{4\text{y}-4-3\text{y}+6}{12}=1$
$\Rightarrow\frac{\text{y}+2}{12}=1$
$\Rightarrow\text{y}+2=12$
$\Rightarrow\text{y}=12-2=10$
$\Rightarrow\text{y}=10$
Check: $\text{L.H.S.}=\frac{\text{y}-1}{3}-\frac{\text{y}-2}{4}$
$=\frac{10-1}{3}-\frac{10-2}{4}$
$=\frac{9}{3}-\frac{8}{4}=3-2$
$=1$
$=\text{R.H.S. = L.H.S.}$ Hence $= \text{y}=10$
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