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# Solve the following equations: (a) 2(x + 4) = 12

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

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(a) We have:

2(x + 4) = 12

Dividing both sides by 2,  we have :

$x\ +\ 4\ =\ 6$

Transposing 4 to the RHS, we get  :

$x\ =\ 6\ -\ 4\ =\ 2$

Thus  $x\ =\ 2$

(b)  We have:

3(n – 5) = 21

Dividing both sides by 3,  we have :

$n\ -\ 5\ =\ 7$

Transposing - 5 to the RHS, we get  :

$n\ =\ 7\ +\ 5\ =\ 12$

Thus  $n\ =\ 12$

(c)  We have   :

3(n – 5) = – 21

Dividing both sides by 3,  we have :

$n\ -\ 5\ =\ -\ 7$

Transposing - 5 to the RHS, we get  :

$n\ =\ -\ 7\ +\ 5\ =\ -\ 2$

Thus  $n\ =\ -\ 2$

(d) We have   :

– 4(2 + x) = 8

Dividing both sides by - 4,  we have :

$x\ +\ 2\ =\ -\ 2$

Transposing 2 to the RHS, we get  :

$x\ =\ -\ 2\ -\ 2\ =\ -\ 4$

Thus  $x\ =\ -\ 4$

(e)  We have   :

4(2 - x) = 8

Dividing both sides by  4,  we have :

$2\ -\ x\ =\ 2$

Transposing x to the RHS and 2 to the LHS , we get  :

$x\ =\ 2\ -\ 2\ =\ 0$

Thus  $x\ =\ 0$

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