Question
$\frac{6\text{x}-2}{9}+\frac{3\text{x}+5}{18}=\frac13$
✓
Answer
$\frac{6\text{x}-2}{9}+\frac{3\text{x+5}}{18}=\frac13$
$=\frac{6\text{x}(2)-2(2)+\text{3x}+5}{18}=\frac13$
$=\frac{12\text{x}-4+3\text{x}+5}{18}=\frac13$
$=\frac{15\text{x}+1}{18}=\frac13$
Multiplying both sides by 18, we get
$=\frac{15\text{x}+1}{18}\times18=\frac12\times18$
$=15\text{x}+1=6$
Transposing 1 to R.H.S., we get
= 15x = 6 - 1
= 15x = 5
Dividing both sides by 15, we get
$=\frac{15\text{x}}{15}=\frac{5}{15}$
$=\text{x}=\frac13$
Verification:
Substituting $\text{x}=\frac13$ both sides, we get
$\frac{6\big(\frac13\big)-2}{9}+\frac{3\big(\frac13\big)+5}{18}=\frac13$
$\frac{2-2}{9}+\frac{1+5}{18}=\frac13$
$0+\frac{6}{18}=\frac13$
$\frac13=\frac13$
L.H.S. = R.H.S.
Hence, verified.
$=\frac{6\text{x}(2)-2(2)+\text{3x}+5}{18}=\frac13$
$=\frac{12\text{x}-4+3\text{x}+5}{18}=\frac13$
$=\frac{15\text{x}+1}{18}=\frac13$
Multiplying both sides by 18, we get
$=\frac{15\text{x}+1}{18}\times18=\frac12\times18$
$=15\text{x}+1=6$
Transposing 1 to R.H.S., we get
= 15x = 6 - 1
= 15x = 5
Dividing both sides by 15, we get
$=\frac{15\text{x}}{15}=\frac{5}{15}$
$=\text{x}=\frac13$
Verification:
Substituting $\text{x}=\frac13$ both sides, we get
$\frac{6\big(\frac13\big)-2}{9}+\frac{3\big(\frac13\big)+5}{18}=\frac13$
$\frac{2-2}{9}+\frac{1+5}{18}=\frac13$
$0+\frac{6}{18}=\frac13$
$\frac13=\frac13$
L.H.S. = 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
In the given figure, two straight line AB and CD intersect at a point O. If $\angle\text{AOC} = 42^\circ,$ find the measure of each of the angles:
→
- $\angle\text{AOD}$
- $\angle\text{BOD}$
- $\angle\text{COB}$
Construct an equilateral triangle each of whose sides measures 6.2cm. Measure each of its angles.
Construct $\triangle\text{ABC}$ in which BC = 4cm, $\angle\text{B}=50^\circ$ and $\angle\text{C}=70^\circ.$
→Which two consecutive even numbers have an LCM of 180 ?
Find x, y, z (whichever is required) from the figure given below:
$\text{x}-\frac{\text{x}}{4}-\frac{1}{2}=3+\frac{\text{x}}{4}$
→A room 5 m long and 4 m wide is surrounded by a verandah. If the verandah occupies an area of $22 m^2$, find the width of the varandah.
→A man goes 3km due north and then 4km due east. How far is he away from his initial position?
The ages of Sonal and Manoj are in the ratio 7 : 5 Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.
Calculate the area of the quadrilateral ABCD as shown in Figure, given that BD = 42cm, AC = 28cm, OD = 12cm and $\text{AC}\bot\text{BO}.$
→