Question
Solve : $\frac{2 x}{3}-\frac{3 x}{8}=\frac{7}{12}$
✓
Answer
$\frac{2 x}{3}-\frac{3 x}{8}=\frac{7}{12}$
$\text{L.C.M}$. of $3$ and $8=2 \times 2 \times 2 \times 3=24$
$\therefore \frac{2 \mathrm{x} \times 8}{3 \times 8}-\frac{3 \mathrm{x} \times 3}{8 \times 3}=\frac{7}{12}$
$=\frac{16 \mathrm{x}}{24}-\frac{9 \mathrm{x}}{24}=\frac{7}{12}$
$=\frac{16 x}{24}-\frac{9 x}{24}=\frac{7}{12}$
$=\frac{16 x-9 x}{24}=\frac{7}{12}$
$=\frac{7 \mathrm{x}}{24}=\frac{7}{12}$
$=\mathrm{x}=\frac{7 \times 24}{12 \times 7}=2$
$\therefore x=2$
$\text{L.C.M}$. of $3$ and $8=2 \times 2 \times 2 \times 3=24$
$\therefore \frac{2 \mathrm{x} \times 8}{3 \times 8}-\frac{3 \mathrm{x} \times 3}{8 \times 3}=\frac{7}{12}$
$=\frac{16 \mathrm{x}}{24}-\frac{9 \mathrm{x}}{24}=\frac{7}{12}$
$=\frac{16 x}{24}-\frac{9 x}{24}=\frac{7}{12}$
$=\frac{16 x-9 x}{24}=\frac{7}{12}$
$=\frac{7 \mathrm{x}}{24}=\frac{7}{12}$
$=\mathrm{x}=\frac{7 \times 24}{12 \times 7}=2$
$\therefore x=2$
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
$\text{PQRS}$ is a parallelogram whose diagonals intersect at $M$. If $\angle PMS = 54^\circ , \angle QSR = 25^\circ$ and $\angle SQR = 30^\circ$ ; find : $(i)\ \angle RPS\ (ii)\ \angle PRS\ (iii)\ \angle PSR.$
→Solve and graph the solution set on a number line : $\frac{2}{3} \mathrm{x}+5 \leq \frac{1}{2} \mathrm{x}+6 ; \mathrm{x} \in \mathrm{W}$
→Given the universal set $= \{x : x \in N$ and $x < 20\}$, find : $A = \{x : x = 3p ; p \in N\}$
→State, if the following pair of a set is equal or not : $M = \{x : x \in W$ and $x + 3 < 8\}$ and $N = \{y : y = 2n -1, n \in N$ and $n < 5\}$
→$A$ and $B$ complete a piece of work in $24$ days. $B$ and $C$ do the same work in $36$ days; and $A, B$, and $C$ together finish it in $18$ days. In how many days will : $(i)\ A$ alone, $(ii)\ C$ alone,$\ (iii)\ A$ and $C$ together, complete the work?
→Construct a quadrilateral $\text{ABCD}$, such that $AB = BC = CD = 4.4 \ cm, \angle B = 90^\circ$ and $\angle C = 120^\circ$ .
→John lent $Rs. 2550$ to Mohan at $7.5$ percent per annum. If Mohan discharges the debt after $8$ months by giving an old black and white television and $Rs. 1422.50\ ;$ find the price of the television.
→Given $A = \{0, 1, 2, 4, 5\}, B = \{0, 2, 4, 6, 8\}$ and $C = \{0, 3, 6, 9\}$. Show that $A ∪ (B ∪ C) = (A ∪ B) ∪ C$ i.e. the union of sets is associative.
→Find the quotient and the remainder when : $a^3− 5a^2 + 8a + 15$ is divided by $a + 1$. verify your answer.
→Construct a quadrilateral $\text{ABCD}\ ;$ if : $AB = 4.3 \ cm, BC = 5.4, CD = 5 \ cm, DA = 4.8 \ cm$ and angle $ABC = 75^\circ .$
→