Linear Equations
Exercise 2.1 (NCERT)
Solve the following equations:
Question 1: `x-2=7`
Solution: Given `x-2=7`
By adding 2 to both sides we get:
`x-2+2=7+2`
Or, `x=9`
Question 2: `y+3=10`
Solution: Given `y+3=10`
By subtracting 3 from both sides we get:
`y+3-3=10-3`
Or, `y=7`
Question 3: `6=z+2`
Solution: Given `6=z+2`
By subtracting 2 from both sides we get:
`6-2=z+2-2`
Or, `4=z`
Or, `z=4`
Question 4: `3/7+x=(17)/(7)`
Solution: Given `3/7+x=(17)/(7)`
By subtracting `3/7` from both sides we get:
`3/7+x-3/7=(17)/(7)-3/7`
Or, `x+3/7-3/7=(17)/(7)-3/7`
Or, `x=(17-3)/(7)=(14)/(7)=2`
Question 5: `6x=12`
Solution: Given `6x=12`
After dividing both sides by 6 we get:
`(6x)/(6)=(12)/(6)`
Or, `x=2`
Question 6: `t/5=10`
Solution: Given `t/5=10`
By multiplying both sides by 5 we get:
`t/5xx5=10xx5`
Or, `t=50`
Question 7: `(2x)/(3)=18`
Solution: Given `(2x)/(3)=18`
By multiplying both sides by 3 we get:
`(2x)/(3)xx3=18xx3`
Or, `2x=54`
By dividing both sides by 2 we get:
`(2x)/(2)=(54)/(2)`
Or, `x=27`
Question 8: `1.6=(y)/(1.5)`
Solution: Given `1.6=(y)/(1.5)`
By multiplying both sides by 1.5 we get:
`1.6xx1.5=(y)/(1.5)xx1.5`
Or, `2.4=y`
Or, `y=2.4`
Question 9: `7x-9=16`
Solution: Given `7x-9=16`
By adding 9 on both sides we get:
`7x-9+9=16+9`
Or, `7x=25`
By dividing both sides by 7 we get:
`(7x)/(7)=(25)/(7)`
Or, `x=(25)/(7)`
Question 10: `14y-8=13`
Solution: Given `14y-8=13`
Adding 8 on both sides we get:
`14y-8+8=13+8`
Or, `14y=21`
Dividing both sides by 14 we get:
`(14y)/(14)=(21)/(14)`
Or, `y=3/2`
Question 11: `17+6p=9`
Solution: Given `17+6p=9`
Subtracting 17 from both sides we get:
`17+6p-17=9-17`
Or, `6p+17-17=-8`
Or, `6p=-8`
Dividing both sides by 6 we get:
`(6p)/(6)=(-8)/(6)`
Or, `p=-4/3`
Question 12: `x/3+1=(7)/(15)`
Solution: Given `x/3+1=(7)/(15)`
Subtracting 1 from both sides we get:
`x/3+1-1=(7)/(15)-1`
Or, `x/3=(7-15)/(15)`
Or, `x/3=(-8)/(15)`
Multiplying both sides by 3 we get:
`x/3xx3=(-8)/(15)xx3`
Or, `x=-8/5`