SOLUTION: Hi, 3 problems 1/2 (x + 5)=1/3 x +1/4 7=2(y+6) 0.04x + 0.08(20-x)=1.4 Thank you so much for being here. Your help is greatly appreciated

Question 106356This question is from textbook
: Hi,
3 problems
1/2 (x + 5)=1/3 x +1/4
7=2(y+6)
0.04x + 0.08(20-x)=1.4
Thank you so much for being here. Your help is greatly appreciated This question is from textbook

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

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