Linear Equations

Extra Questions

Question 1: Solve `5x + 3 = 13`

Solution: First method

We have `5x + 3 = 13`
By subtracting 3 in both side we get
`⇒ 5x + 3 – 3 = 13 – 3`
`⇒ 5x + 0 = 10`
`⇒ 5x = 10`
On dividing both side by 5 we get

`(5x)/(5)=(10)/(5)`

Or, `x=2`

Second method:

We have `5x + 3 = 13`
On transposing 3 to right hand side of equation we get
`⇒ 5x = 13 – 3`
`⇒ 5x = 10`
On dividing both side by 5 we get

`(5x)/(5)=(10)/(5)`

Or, `x=2`


Question 2: Solve `10 m – 5 = 35`

Solution:
We have `10 m – 5 = 35`
On transposing – 5 to right hand side we get
`⇒ 10 m = 35 + 5`
`⇒ 10 m = 40`
On dividing both side by 10 we get

`(10 m)/(10)=(40)/(10)`

Or, `m=4`

Question 3: Solve `4a – 30 = 10`

Solution:
We have `4a – 30 = 10`
On transposing – 30 to RHS we get
`⇒ 4a = 10 + 30`
`⇒ 4a = 40`
On dividing both side by 4 we get

`(4 a)/(4)=(40)/(4)`

Or, `a=10`

Question 4: Solve `40 a + 10 = 20`

Solution:
We have `40 a + 10 = 20`
On transposing 10 to RHS we get
`⇒ 40a = 20 – 10`
`⇒ 40a = 10`
On dividing both side by 40 we get

`(40a)/(40)=(10)/(40)`

Or, `a=1/4`


Question 5: Solve `15 m + 30 = 20 – 5`

Solution:
We have `15 m + 30 = 20 – 5`
`⇒ 15 m + 30 = – 15`
On transposing 30 to RHS we get
`⇒ 15 m = – 15 – 30`
`⇒ 15 m = – 45`
On dividing both side by 15 we get

`(15m)/(15)=(-45)/(15)`

Or, `m=-3`

Question 6: Solve `45 x + 30 = 120`

Solution:
We have `45 x + 30 = 120`
On transposing 30 to RHS we get
`⇒ 45 x = 120 – 30`
`⇒ 45 x = 90`
On dividing both side by 45 we get

`(45x)/(45)=(90)/(2)`

Or, `x=2`

Question 7: Sovle `50 + 25 m = 500`

Solution:
We have `50 + 25 m = 500`
On transposing 50 to RHS we get
`⇒ 25 m = 500 – 50`
`⇒ 25 m = 450`
On dividing both side by 25 we get

`(25m)/(25)=(450)/(25)`

Or, `m=18`

Question 8: Solve `65 = 4 b + 5`

Solution:
We have `65 = 4 b + 5`
On transposing 5 to LHS we get
`⇒ 65 – 5 = 4 b`
`⇒ 60 = 4 b`
On dividing both side by 4 we get

`(60)/(4)=(4b)/(4)`

Or, `b=4`



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