Question
Solve the linear equation: $m - \frac{{m - 1}}{2} = 1 - \frac{{m - 2}}{3}$
✓
Answer
m - $\frac{{m - 1}}{2} = 1 - \frac{{m - 2}}{3}$
It is a linear equation since it involves linear expressions only.
$\therefore$ $m - \frac{m}{2} + \frac{1}{2} = 1 - \frac{m}{3} + \frac{2}{3}$
$\therefore$ $m - \frac{m}{2} + \frac{m}{3} = 1 + \frac{2}{3} - \frac{1}{2}$ ... [Transposing $\frac{{ - m}}{3}$ to $L.H.S$. and $\frac{1}{2}$ to $R.H.S.]$
$\therefore$ $\frac{{6m - 3m + 2m}}{6} = \frac{{6 + 4 - 3}}{6}$
$\therefore$ $\frac{{5m}}{6} = \frac{7}{6}$
$\therefore$ m = $\frac{7}{6} \times \frac{6}{5}$ ... [Multiplying both sides by $\frac{6}{5}$]
$\therefore$ m = $\frac{7}{5}$ this is the required solution.
It is a linear equation since it involves linear expressions only.
$\therefore$ $m - \frac{m}{2} + \frac{1}{2} = 1 - \frac{m}{3} + \frac{2}{3}$
$\therefore$ $m - \frac{m}{2} + \frac{m}{3} = 1 + \frac{2}{3} - \frac{1}{2}$ ... [Transposing $\frac{{ - m}}{3}$ to $L.H.S$. and $\frac{1}{2}$ to $R.H.S.]$
$\therefore$ $\frac{{6m - 3m + 2m}}{6} = \frac{{6 + 4 - 3}}{6}$
$\therefore$ $\frac{{5m}}{6} = \frac{7}{6}$
$\therefore$ m = $\frac{7}{6} \times \frac{6}{5}$ ... [Multiplying both sides by $\frac{6}{5}$]
$\therefore$ m = $\frac{7}{5}$ this is the required solution.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
How many soap cakes can be placed in a box of size $56 \ cm × 0.4\ m × 0.25\ m,$ it the size of soap cake is $7\ cm × 5 \ cm × 2.5\ cm?$
→Simplify following: $\text{x}^2 − 3\text{x} + 5 − \frac{1}{2} (3\text{x}^2 − 5\text{x} + 7)$
→Solve the following equations :
$\frac{2 x}{3}+1=\frac{7 x}{15}+3.$
→$\frac{2 x}{3}+1=\frac{7 x}{15}+3.$
Find following product: $ (-5 x y) \times\left(-3 x^2 y z\right) $
→A pipe can fill a cistern in $9$ hours. Due to a leak in its bottom, the cistern fills up in $10$ hours. If the cistern is full, in how much time will it be emptied by the leak?
→A pipe can fill a cistern in $9$ hours. Due to a leak in its bottom, the cistern fills up in $10$ hours. If the cistern is full, in how much time will it be emptied by the leak?
→Ravi can do a piece of work in $15$ hours while Raman can do it in $12$ hours. How long will both take to do it, working together?
→Show that $y=4$ is a solution of the equation
$ y+7-\frac{8 y}{3}=\frac{17}{6}-\frac{5 y}{8} $
→$ y+7-\frac{8 y}{3}=\frac{17}{6}-\frac{5 y}{8} $
The given graph represents the total runs scored by two batsmen $A$ and $B$, during each of the ten different matches in the year $2007.$ Study the graph and answer the following question:
Among the two batsmen, who is steadier? How do you judge it?
→Among the two batsmen, who is steadier? How do you judge it?
Simplify: $\frac{5}{26}+\frac{11}{-39}$
→