Question
Solve the following equations. Check your result in case.
$\frac{3}{4}(7\text{x}-1)-\Big(2\text{x}-\frac{1-\text{x}}{2}\Big)=\text{x}+\frac{3}{2}$
$\frac{3}{4}(7\text{x}-1)-\Big(2\text{x}-\frac{1-\text{x}}{2}\Big)=\text{x}+\frac{3}{2}$
✓
Answer
$\frac{3}{4}(7\text{x}-1)-\Big(2\text{x}-\frac{1-\text{x}}{2}\Big)=\text{x}+\frac{3}{2}$
$\Rightarrow\frac{3(7\text{x}-1)}{4}-\frac{4\text{x}-1+\text{x}}{2}=\frac{2\text{x}+3}{2}$
$\Rightarrow\frac{21\text{x}-3}{4}-\frac{5\text{x}-1}{2}=\frac{2\text{x}+3}{2}$
$=\frac{21\text{x}-3-10\text{x}+2=4\text{x}+6}{4}$ (LCM 4, 2 = 4)
$\Rightarrow21\text{x}-10\text{x}-4\text{x}=6+3-2$
(By transposing)
$\Rightarrow7\text{x}=7$
$\Rightarrow\text{x}=\frac{7}{7}=1$
$\therefore\text{x}=1$
Check:
$\frac{3}{4}(7\text{x}-1)-\Big[2\text{x}-\frac{1-\text{x}}{2}\Big]$
$=\frac{3}{4}(7\times1-1)-\Big[2\times1-\frac{1-1}{2}\Big]$
$=\frac{3\times6}{4}-(2-0)=\frac{18}{4}-2$
$=\frac{9}{2}-2=\frac{9-4}{2}=\frac{5}{2}$
$\text{R.H.S.}=\text{x}+\frac{3}{2}$
$=1+\frac{3}{2}$
$=\frac{2+3}{2}=\frac{5}{2}$
$\therefore\text{L.H.S. = R.H.S.}$
Hence $\text{x}=1$
$\Rightarrow\frac{3(7\text{x}-1)}{4}-\frac{4\text{x}-1+\text{x}}{2}=\frac{2\text{x}+3}{2}$
$\Rightarrow\frac{21\text{x}-3}{4}-\frac{5\text{x}-1}{2}=\frac{2\text{x}+3}{2}$
$=\frac{21\text{x}-3-10\text{x}+2=4\text{x}+6}{4}$ (LCM 4, 2 = 4)
$\Rightarrow21\text{x}-10\text{x}-4\text{x}=6+3-2$
(By transposing)
$\Rightarrow7\text{x}=7$
$\Rightarrow\text{x}=\frac{7}{7}=1$
$\therefore\text{x}=1$
Check:
$\frac{3}{4}(7\text{x}-1)-\Big[2\text{x}-\frac{1-\text{x}}{2}\Big]$
$=\frac{3}{4}(7\times1-1)-\Big[2\times1-\frac{1-1}{2}\Big]$
$=\frac{3\times6}{4}-(2-0)=\frac{18}{4}-2$
$=\frac{9}{2}-2=\frac{9-4}{2}=\frac{5}{2}$
$\text{R.H.S.}=\text{x}+\frac{3}{2}$
$=1+\frac{3}{2}$
$=\frac{2+3}{2}=\frac{5}{2}$
$\therefore\text{L.H.S. = R.H.S.}$
Hence $\text{x}=1$
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
A rectangular field is measured 290m by 210m. How long will it take for a girl to go two times round the field, if she walks at the rate of 1.5m/sec?
Simplify:
$(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x+y)$
→$(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x+y)$
A rectangular plot of land measures 95 m by 72 m . Inside the plot, a path of uniform width of 3.5 m is to be constructed all around. The rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at Rs 80 per $m ^2$ and laying the grass at Rs 40 per $m ^2$.
→Draw an equilateral triangle with side 6.5 cm.
Solve the following equations. Check your result in case.
t - (2t + 5) - 5(1 - 2t) = 2(3 + 4t) - 3(t - 4)
t - (2t + 5) - 5(1 - 2t) = 2(3 + 4t) - 3(t - 4)
A wire is in the shape of a rectangle. Its length is 40cm and breadth is 22cm. If the same wire is bent in the shape of a square, what will be the measure of each side? Also, find which side encloses more area?
In Figure, measures of some angles are indicated. Find the value of x.
Draw $\triangle\text{ABC}$ in which $\angle\text{A}=120^\circ,$ AB = AC = 3cm. Measure $\angle\text{B}$ and $\angle\text{C}.$
→AC, AD and AE are joined. Find.
$\angle \text{FAB}+\angle \text{ABC}+\angle \text{BCD}+\angle \text{CDE} +\angle \text{DEF}+\angle \text{EFA}$
→$\angle \text{FAB}+\angle \text{ABC}+\angle \text{BCD}+\angle \text{CDE} +\angle \text{DEF}+\angle \text{EFA}$
Arrange the following rational numbers in descending order:
$\frac{17}{-30},\frac{11}{-15},\frac{-7}{10},\frac{10}{5}$
→$\frac{17}{-30},\frac{11}{-15},\frac{-7}{10},\frac{10}{5}$