Question
$\frac{\text{x}}{2}+\frac32=\frac{2\text{x}}{5}-1$
✓
Answer
$\frac{\text{x}}{2}+\frac{3}{2}=\frac{2\text{x}}5-1{}$
Transposing $\frac{2\text{x}}{5}$ to $L.H.S$. and $\frac32$ to $R.H.S$., we get
$=\frac{\text{x}}{2}-\frac{2\text{x}}{5}=-1-\frac32$
$=\frac{5\text{x}-4\text{x}}{10}=\frac{-2-3}{2}$
$=\frac{\text{x}}{10}=\frac{-5}{2}$
Multiplying both sides by $10,$ we get
$=\frac{\text{x}}{10}\times10=\frac{-5}{2}\times10$
$=\text{x}=-25$
Verification: Substituting $x = -25$ in the given equation, we get
$\frac{-25}{2}+\frac32=\frac{2(-25)}{5}-1$
$\frac{-22}{2}=-10-1$
$-11=-11$
$\text{L.H.S.}=\text{R.H.S.}$ Hence, verified.
Transposing $\frac{2\text{x}}{5}$ to $L.H.S$. and $\frac32$ to $R.H.S$., we get
$=\frac{\text{x}}{2}-\frac{2\text{x}}{5}=-1-\frac32$
$=\frac{5\text{x}-4\text{x}}{10}=\frac{-2-3}{2}$
$=\frac{\text{x}}{10}=\frac{-5}{2}$
Multiplying both sides by $10,$ we get
$=\frac{\text{x}}{10}\times10=\frac{-5}{2}\times10$
$=\text{x}=-25$
Verification: Substituting $x = -25$ in the given equation, we get
$\frac{-25}{2}+\frac32=\frac{2(-25)}{5}-1$
$\frac{-22}{2}=-10-1$
$-11=-11$
$\text{L.H.S.}=\text{R.H.S.}$ Hence, verified.
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
By selling $8$ dozen pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain percent.
→Ratio of the area of $\triangle\text{WXY}$ to the area of $\triangle\text{WZY}$ is $3 : 4.$ If the area of $\triangle\text{WXZ}$ is $56cm^2$ and $WY = 8cm$, find the lengths of $XY$ and $YZ.$
→Find three consecutive natural numbers such that the sum of the first and second is 15 more than the third.
The ratio of the radii of two circles is $4 : 5.$ Find the ratio of their areas.
→Solve the following equations. Check your result in case. $6(3x + 2) - 5(6x - 1) = 3(x - 8) - 5(7x - 6) + 9x$
→Evaluate: $\frac{11}{-12}+\frac{3}{-8}+\frac{1}{4}$
→Find the mode of
$2,14,16,12,14,14,16,14,10,14,18,14$.
→$2,14,16,12,14,14,16,14,10,14,18,14$.
In $12.76, A B \| C D$. Find the values of $x, y, z$.
→Rita has bought a carpet of size $4\text{m}\times6\frac{2}{3}\text{m}$ But her room size is $3\frac{1}{3}\text{m}\times5\frac{1}{3}\text{m}$ What fraction of area should be cut off to fit wall to wall carpet into the room?
→A number is increased by $10\%$ and the increased number is decreased by $10\%$. Show that the net decrease is $1\%.$
→