More math problem question. :/?

Question

See I'm a English major so math is not my strong suite. 


6(r+2)-4=-10 

The furthest I got with that was: 

2(r+2)=-10 


5-1/2(x-6)=4 


4(2a-1)=-10(a-5) 


2(w-3)+5=3(w-1) 

Answer 1

• The expression 6(r + 2) - 4 = - 10

Apply distributive property a(b + c) = ab + ac

6(r) + 6(2) - 4 = - 10

6r + 12 - 4 = - 10

6r = - 10 - 8

6r = -18

Divide each side by 6.

6r/6 = - 18/6

Solution r = - 3.

• The expression 2(r + 2) = - 10

Apply distributive property a(b + c) = ab + ac

2(r) + 2(2) = - 10

2r + 4 = - 10

2r = - 10 - 4

2r = - 14

Divide each side by 2.

2r/2 = - 14/2

Solution r = - 7.

• The expression 5 - 1/2(x - 6) = 4

Lest common multiple of 1 and 2(x - 6) is 2(x - 6).

[ 5(2)(x - 6) - 1]/2(x - 6) = 4

[ 10(x - 6) - 1]/(2x - 12) = 4

[ 10x - 60 - 1] = 4(2x - 12)

10x - 61 = 8x - 48

10x - 8x = - 48 + 61

2x = 13

Solution x = 13/2.

Answer 2

• The expression 4(2a -1) = - 10(a - 5)

Apply distributive property a(b + c) = ab + ac

4(2a) + 4(-1) = (- 10)(a) + (- 10)(- 5)

8a - 4 = - 10a + 50

8a + 10a = 50 + 4

18a = 54

Divide each side by 18.

18a/18 = 54/18

a = 3

• The expression 2(w - 3) + 5 = 3(w - 1)

Apply distributive property a(b + c) = ab + ac

2(w) - 2(3) + 5 = 3(w) + 3(- 1)

2w - 6 + 5 = 3w - 3

2w - 1 = 3w - 3

3w - 2w = - 1 + 3

w = 2.