Question 106356
1) 
1/2 (x + 5)=1/3 x +1/4  multiply each term by 12, since 12 is the LCM---the smallest number that 2, 3 and 4 divides evenly into.  This will get rid of the fractions

12*(1/2)(x+5)=12*(1/3)x+12*(1/4)  simplify

6(x+5)=4x+3  get rid of parens

6x+30=4x+3  subtract 4x and also 30 from both sides

6x-4x+30-30=4x-4x+3-30  collect like terms

2x=-27  divide both sides by 2

x=-13.5

CK
1/2(-13.5+5)=(1/3)(-13.5)+1/4
1/2(-8.5)=1/3(-13.5)+0.25
-4.25=-4.5+0.25
-4.25=-4.25

2)
7=2(y+6) get rid of parens

7=2y+12  subtract 12 from both sides

7-12=2y+12-12  collect like terms

-5=2y  divide both sides by 2

y=-2.5

CK
7=2(-2.5+6)

7=-5+12
7=7


3)

0.04x + 0.08(20-x)=1.4 
Lets just multiply each term by 100 and we will not have to deal with decimals.
---And we get:

4x+8(20-x)=140  get rid of parens

4x+160-8x=140  subtract 160 from both sides

4x+160-160-8x=140-160  collect like terms

-4x=-20  divide both sides by -4
x=5

CK
0.04*5+0.08(20-5)=1.4
0.2+1.2=1.4
1.4=1.4

ok, we'll also do the decimal version:
0.04x + 0.08(20-x)=1.4  get rid of parens

0.04x+1.6-0.08x=1.4  subtract 1.6 from both isdes

0.04x+1.6-1.6-0.08x=1.4-1.6  collect like terms

-0.04x=-0.2  divide both sides by -0.04

x=5


Hope this helps---ptaylor