Question
Solve the following equation and verify your answer: $\frac{3\text{x}+5}{2\text{x}+7}=4$
✓
Answer
$\frac{3\text{x}+5}{2\text{x}+7}=\frac{4}{1}$
By cross multiplication:
$4(2\text{x}+7)=1\times(3\text{x}+5)$
$8\text{x}+28=3\text{x}+5$
$8\text{x}-3\text{x}=5-28$ (By transposition)
$\Rightarrow5\text{x}=-23$
$\Rightarrow\text{x}=\frac{-23}{5}$
$\text{x}=\frac{-23}{5}$Verification:
$\text{L.H.S.}=\frac{3\text{x}+5}{2\text{x}+7}=\frac{3\Big(\frac{-23}{5}\Big)+5}{2\Big(\frac{-23}{5}\Big)+7}$
$=\frac{\frac{-69}{5}+5}{\frac{-46}{5}+7}=\frac{\frac{-69+25}{5}}{\frac{-46+35}{5}}=\frac{\frac{-44}{5}}{\frac{-11}{5}}$
$\frac{-44}{5}\times\frac{-5}{11}=4=\text{R.H.S.}$
By cross multiplication:
$4(2\text{x}+7)=1\times(3\text{x}+5)$
$8\text{x}+28=3\text{x}+5$
$8\text{x}-3\text{x}=5-28$ (By transposition)
$\Rightarrow5\text{x}=-23$
$\Rightarrow\text{x}=\frac{-23}{5}$
$\text{x}=\frac{-23}{5}$Verification:
$\text{L.H.S.}=\frac{3\text{x}+5}{2\text{x}+7}=\frac{3\Big(\frac{-23}{5}\Big)+5}{2\Big(\frac{-23}{5}\Big)+7}$
$=\frac{\frac{-69}{5}+5}{\frac{-46}{5}+7}=\frac{\frac{-69+25}{5}}{\frac{-46+35}{5}}=\frac{\frac{-44}{5}}{\frac{-11}{5}}$
$\frac{-44}{5}\times\frac{-5}{11}=4=\text{R.H.S.}$
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
Simplify:
$ \left(2 x^2+3 x-5\right)\left(3 x^2-5 x+4\right) $
→$ \left(2 x^2+3 x-5\right)\left(3 x^2-5 x+4\right) $
$A$ and $B$ can finish a work in $20$ days. $A$ alone can do $\frac{1}{5}\text{th}$ of the work in $12$ days. In how many days can $B$ alone do it?
→The ages of sonu and Monu are in the ratio $7 : 5$. Ten years hence, the ratio of their ages will be $9 : 7$. Find their present ages.
→Jitendra set up a factory by investing $Rs. 2500000$. During the first two successive years his profits were $5\%$ and $10\%$ respectively. If each year the profit was on previous year's capital, compute his total profit.
→A field is $150m$ long and $100m$ wide. A plot (outside the field) $50m$ long and $30m$ wide is dug to a depth of $8m$ and the earth taken out from the plot is spread evenly in the field. By how much the level of field is raised?
→Draw a histogram for the frequency distribution of following data:
→|
Class interval
|
$20-25$
|
$25-30$
|
$30-35$
|
$35-40$
|
$40-45$
|
$45-50$
|
|
Frequency
|
$30$
|
$24$
|
$52$
|
$28$
|
$46$
|
$10$
|
Find the area of the following regular hexagon.
Draw a pie-diagram for the following data of the investment pattern in a five year plan:
→|
Agriculture
|
Irrigation and Power | Small Industries |
Transport
|
Social service
|
Miscellaneous
|
|
$14\%$
|
$16\%$
|
$29\%$
|
$17\%$
|
$16\%$
|
$8\%$
|
$ABCD$ is a rhombus whose diagonals intersect at $O$. If $AB = 10\ cm$, diagonal $BD = 16\ cm$, find the length of diagonal $AC$.
→Find the compound interest on $Rs. 15625$ for $9$ months, at $16\%$ per annum, compounded quarterly.
→