# 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`