**Simple Equations**

**Question 1.****Give first the step you will use to separate the variable and then solve the equation :(a)** x – 1 = 0

**(b)**x + 1= 0

**(c)**x – 1 = 5

**(d)**x + 6 = 2

**(e)**y – 4 = -7

**(f)**y – 4 = 4

**(g)**y + 4 = 4

**(h)**y – 4 = -4

**Solution:****(a)** We have, x – 1 = 0

In order to solve this equation, we have to get x by itself on the L.H.S. To get x by itself on the L.H.S., we need to shift -1. This can be done by adding 1 to both sides of the given equation.

x – 1 + 1 = 0 + 1 [ Adding 1 to both sides ]

x = 1 [ ∵ -1 + 1 = 0 and 0 + 1 = 1 ]

**(b)** We have, x + 1 = 0

In order to get x by itself on the L.H.S., we need to shift 1. This can be done by subtracting 1 from both sides of the given equation.

x + 1 – 1 = 0 – 1 [Subtracting 1 from both sides]

⇒ x = -1 [∵ 1 – 1 = 0, 0 – 1 = -1 ]

So, x = -1 is the solution of the given equation.

**(c)** We have, x – 1 = 5

In order to solve this equation, we have to get x by itself on the L.H.S. To get x by itself on the L.H.S., we need to shift -1. This can be done by adding 1 to both sides of the given equation.

**(d)** We have, x + 6 = 2

In order to solve this equation, we have to get x by itself on the L.H.S. To get x by itself on the L.H.S., we need to shift 6. This can be done by subtracting 6 from both sides of the given equation.

**(e)** We have, y – 4 = -7

In order to solve this equation, we have to get y by itself on the L.H.S. To get y by itself on the L.H.S.,we need to shift -4. This can be done by adding 4 to both sides of the given equation.

**(f)** We have, y – 4 = 4

In order to solve this equation, we have to get y by itself on the L.H.S. To get y by itself on the L.H.S., we need to shift -4. This can be done by adding 4 to both sides of the given equation.

**(g)** We have, y + 4 = 4

In order to solve this equation, we have to get y by itself on the L.H.S. To get y by itself on the L.H.S., we need to shift 4. This can be done by subtracting 4 from both sides of the given equation.

**(h)** We have, y + 4 = -4

In order to solve this equation, we have to get y by itself on the L.H.S. To get y by itself on the L.H.S., we need to shift 4. This can be done by subtracting 4 from both sides of the given equation.

**Question 2.****Give first the step you will use to separate the variable and then solve the equation :(a)** 3l = 42

**(b)**= 6

**(c)**= 4

**(d)**4x = 25

**(e)**8y = 36

**(f)**=

**(g)**=

**(h)**20t = -10

**Solution:****(a)** We have, 3l = 42

In order to solve this equation, we have to get l by itself on the L.H.S. For this, 3 has to be removed from the L.H.S. This can be done by dividing both sides of the equation by 3.

**(b)** We have, = 6

In order to solve this equation, we have to get b by itself on the L.H.S. To get b by itself on L.H.S., we have to remove 2 from L.H.S. This can be done by multiplying both sides of the equation by 2. Thus, we have

**(c)** We have, = 4

In order to solve this equation, we have to get p by itself on the L.H.S. To get p by itself on L.H.S., we have to remove 7 from L.H.S. This can be done by multiplying both sides of the equation by 7. Thus, we have

**(d)** We have, 4x = 25

In order to solve this equation, we have to get x by itself on the L.H.S. For this, 4 has to be removed from the L.H.S. This can be done by dividing both sides of the equation by 4.

**(e)** We have, 8y = 36

In order to solve this equation, we have to get y by itself on the L.H.S. For this, 8 has to be removed from the L.H.S. This can be done by dividing both sides of the equation by 8.

**(f)** We have, =

In order to solve this equation,we have to get z by itself on the L.H.S. To get z by itself on L.H.S., we have to remove 3 from L.H.S. This can be done by multiplying both sides of the equation by 3.

Thus, we have

**(g)** We have, =

In order to solve this equation, we have to get a by itself on the L.H.S. To get a by itself on L.H.S., we have to remove 5 from L.H.S. This can be done by multiplying both sides of the equation by 5.

**(h)** We have, 20t = -10

In order to solve this equation, we have to get t by itself on the L.H.S. For this, 20 has to be removed from the L.H.S. This can be done by dividing both sides of the equation by 20.

**Question 3.****Give the steps you will use to separate the variable and then solve the equation :(a)** 3n – 2 = 46

**(b)**5m + 7 = 17

**(c)**= 40

**(d)**= 6

**Solution:**

**Question 4.****Solve the following equations :(a)** 10p = 100

**(b)**10p + 10 = 100

**(c)**= 5

**(d)**= 5

**(e)**= 6

**(f)**3s = -9

**(g)**3s + 12 = 0

**(h)**3s = 0

**(i)**2q = 6

**(j)**2q – 6 = 0

**(k)**2q + 6 = 0

**(l)**2q + 6 = 12

**Solution:**