**Question** 1:

Solve the following equations.

(a) (b) 5*t* + 28 = 10 (c)

(d) (e) (f)

(g) (h) 6*z* + 10 = − 2 (i)

(j)

**Answer**:

(a)

(Transposing to R.H.S.)

Dividing both sides by 2,

(b) 5*t *+ 28 = 10

5*t* = 10 − 28 = −18 (Transposing 28 to R.H.S.)

Dividing both sides by 5,

(c)

(Transposing 3 to R.H.S.)

Multiplying both sides by 5,

*a* = −1 × 5 = −5

(d)

(Transposing 7 to R.H.S.)

Multiplying both sides by 4,

*q* = −8

(e)

Multiplying both sides by 2,

5*x *= −10 × 2 = −20

Dividing both sides by 5,

(f)

Multiplying both sides by 2,

Dividing both sides by 5,

(g)

(Transposing to R.H.S.)

Dividing both sides by 7,

(h) 6*z* + 10 = −2

6*z* = − 2 − 10 = −12 (Transposing 10 to R.H.S.)

Dividing both sides by 6,

(i)

Multiplying both sides by 2,

Dividing both sides by 3,

(j)

(Transposing −5 to R.H.S.)

Multiplying both sides by 3,

2*b* = 8 × 3 = 24

Dividing both sides by 2,

*b* = = 12

**Question** 2:

Solve the following equations.

(a) 2 (*x* + 4) = 12 (b) 3 (*n* − 5) = 21

(c) 3 (*n* − 5) = − 21 (d) −4 (2 + *x*) = 8

(e) 4(2 − *x*) = 8

**Answer**:

(a) 2 (*x* + 4) = 12

Dividing both sides by 2,

*x* = 6 − 4 = 2 (Transposing 4 to R.H.S.)

(b) 3 (*n* − 5) = 21

Dividing both sides by 3,

*n* = 7 + 5 = 12 (Transposing −5 to R.H.S.)

(c) 3 (*n* − 5) = −21

Dividing both sides by 3,

*n* = − 7 + 5 = −2 (Transposing −5 to R.H.S.)

(d) −4 (2 + *x*) = 8

Dividing both sides by −4,

*x* = − 2 − 2 = −4 (Transposing 2 to R.H.S.)

(e) 4 (2 − *x*) = 8

Dividing both sides by 4,

2 − *x* = 2

−*x* = 2 − 2 (Transposing 2 to R.H.S.)

−*x* = 0

*x* = 0

**Question** 3:

Solve the following equations.

(a) 4 = 5 (*p* − 2) (b) − 4 = 5 (*p* − 2)

(c) 16 = 4 + 3 (*t* + 2) (d) 4 + 5 (*p* − 1) = 34

(e) 0 = 16 + 4 (*m* − 6)

**Answer**:

(a) 4 = 5 (*p* − 2)

Dividing both sides by 5,

(b) − 4 = 5 (*p* − 2)

Dividing both sides by 5,

(c) 16 = 4 + 3 (*t* + 2)

16 − 4 = 3 (*t* + 2) (Transposing 4 to L.H.S.)

12 = 3 (*t* + 2)

Dividing both sides by 3,

4 = *t* + 2

4 − 2 = *t* (Transposing 2 to L.H.S.)

2 = *t*

(d) 4 + 5 (*p* − 1) = 34

5 (*p* − 1) = 34 − 4 = 30 (Transposing 4 to R.H.S.)

Dividing both sides by 5,

*p* = 6 + 1 = 7 (Transposing −1 to R.H.S.)

(e) 0 = 16 + 4 (*m* − 6)

0 = 16 + 4*m* − 24

0 = −8 + 4*m*

4*m* = 8 (Transposing −8 to L.H.S)

Dividing both sides by 4,

*m* = 2

**Question** 4:

(a) Construct 3 equations starting with *x* = 2

(b) Construct 3 equations starting with *x* = − 2

**Answer**:

(a) *x* = 2

Multiplying both sides by 5,

5*x* = 10 (i)

Subtracting 3 from both sides,

5*x* − 3 = 10 − 3

5 *x* − 3 = 7 (ii)

Dividing both sides by 2,

(b) *x *= −2

Subtracting 2 from both sides,

*x* − 2 = − 2 − 2

*x* − 2 = −4 (i)

Again, *x *= −2

Multiplying by 6,

6 × *x* = −2 × 6

6*x* = −12

Subtracting 12 from both sides,

6*x* − 12 = − 12 − 12

6*x* − 12 = −24 (ii)

Adding 24 to both sides,

6*x* − 12 + 24 = − 24 + 24

6*x* + 12 = 0 (iii)