**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

**Answer**:

(a) *x* − 1 = 0

Adding 1 to both sides of the given equation, we obtain

*x *− 1 + 1 = 0 + 1

*x* = 1

(b) *x* + 1 = 0

Subtracting 1 from both sides of the given equation, we obtain

*x* + 1 − 1 = 0 − 1

*x* = −1

(c) *x *− 1 = 5

Adding 1 to both sides of the given equation, we obtain

*x* − 1 + 1 = 5 + 1

*x* = 6

(d) *x* + 6 = 2

Subtracting 6 from both sides of the given equation, we obtain

*x* + 6 − 6 = 2 − 6

*x* = −4

(e) *y* − 4 = −7

Adding 4 to both sides of the given equation, we obtain

*y* − 4 + 4 = − 7 + 4

*y* = −3

(f) *y* − 4 = 4

Adding 4 to both sides of the given equation, we obtain

*y* − 4 + 4 = 4 + 4

*y* = 8

(g) *y* + 4 = 4

Subtracting 4 from both sides of the given equation, we obtain

*y* + 4 − 4 = 4 − 4

*y* = 0

(h) *y* + 4 = −4

Subtracting 4 from both sides of the given equation, we obtain

*y* + 4 − 4 = − 4 − 4

*y* = −8

**Question** 2:

Give first the step you will use to separate the variable and then solve the equation:

(a) 3*l *= 42 (b) (c)

(d) 4*x* = 25 (e) 8*y* = 36 (f)

(g) (h) 20*t *= − 10

**Answer**:

(a) 3*l* = 42

Dividing both sides of the given equation by 3, we obtain

*l* = 14

(b)

Multiplying both sides of the given equation by 2, we obtain

*b* = 12

(c)

Multiplying both sides of the given equation by 7, we obtain

*p* = 28

(d) 4*x* = 25

Dividing both sides of the given equation by 4, we obtain

*x* =

(e) 8*y* = 36

Dividing both sides of the given equation by 8, we obtain

*y *=

(f)

Multiplying both sides of the given equation by 3, we obtain

(g)

Multiplying both sides of the given equation by 5, we obtain

(h) 20*t* = −10

Dividing both sides of the given equation by 20, we obtain

**Question** 3:

Give the steps you will use to separate the variable and then solve the equation:

(a) 3*n* − 2 = 46 (b) 5*m* + 7 = 17 (c)

(d)

**Answer**:

(a) 3*n* − 2 = 46

Adding 2 to both sides of the given equation, we obtain

3*n* − 2 + 2 = 46 + 2

3*n* = 48

Dividing both sides of the given equation by 3, we obtain

*n* = 16

(b) 5*m* + 7 = 17

Subtracting 7 from both sides of the given equation, we obtain

5*m* + 7 − 7 = 17 − 7

5*m* = 10

Dividing both sides of the given equation by 5, we obtain

(c)

Multiplying both sides of the given equation by 3, we obtain

Dividing both sides of the given equation by 20, we obtain

(d)

Multiplying both sides of the given equation by 10, we obtain

Dividing both sides of the given equation by 3, we obtain

*p* = 20

**Question** 4:

Solve the following equations:

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

(d) (e) (f) 3*s* = − 9

(g) 3*s* + 12 = 0 (h) 3*s* = 0 (i) 2*q* = 6

(j) 2*q* − 6 = 0 (k) 2*q* + 6 = 0 (l) 2*q* + 6 = 12

**Answer**:

(a) 10 *p* = 100

(b) 10 *p* + 10 = 100

10 *p *+ 10 − 10 = 100 − 10

10 *p* = 90

(c)

(d)

(e)

(f) 3 *s* = −9

(g) 3 *s* + 12 = 0

3 *s* + 12 − 12= 0 − 12

3 *s* = −12

(h) 3 *s* = 0

(i) 2*q* = 6

(j) 2*q* − 6 = 0

2*q* − 6 + 6 = 0 + 6

2*q* = 6

(k) 2*q* + 6 = 0

2*q* + 6 − 6 = 0 − 6

2*q* = −6

(l) 2*q* + 6 = 12

2*q* + 6 − 6 = 12 − 6

2*q* = 6