# 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`