SOLUTION: Please help me with the following equations. Solving a linear equation with several occurances of the variable. Simply your answer as much as possible. Solve the following for

Question 40343: Please help me with the following equations.
Solving a linear equation with several occurances of the variable. Simply your answer as much as possible.
Solve the following for w
2(w- 3)+2w = 14

Solve for x. Write your response as a fraction in lowest terms.
7/4x + 4/3 = 1/4x + 7

Solve the following equation for x. Simply our anwser as much as possible.
-5(x + 8) = 4x + 32

Solve the following for x. Write your answer as a reduced fraction
-2(x-4)+7=-6(8x-6)+x

Solve the following equation for t. Simply your answer as much as possible.
8t-4/5 + 9t-2/2=47

Answer by zeynep(43) (Show Source): You can put this solution on YOUR website!
2(w- 3)+2w = 14 (by using distriutive property we remove the parantheses first)
2w-6+2w=14 (add the w terms on the left side)
4w-6 = 14 (add additive inverse of -6 to both sides to leave w term alone)
4w-6+6=14+6
4w = 40 (divide both sides by 4, to leav w alone)
4w/4=40/4
w=10
-5(x + 8) = 4x + 32 (by using distriutive property we remove the parantheses first)
-5x-40=4x+32 (get all x terms on one side)
-5x-40-4x= 4x+32-4x
-9x-40=32 (add additive inverse of -40 to both sides to leave x term alone)
-9x-40+40=32+40
-9x=72 (divide both sides by -9 to leave x alone)
-9x/9=72/(-9)
x=-8

-2(x-4)+7=-6(8x-6)+x (by using distriutive property we remove the parantheses first)
-2x+8+7=-48x+36+x
-2x+15=-47x+36 (get all x terms on one side)
-2x+15+47x=-47x+36+47x
45x+15=36 (add additive inverse of 15 to both sides to leave x term alone)
45x+15-15=36-15
45x=21 (divide both sides by 45 to leave x term alone)
45x/45=21/45
x=21/45
7/4x + 4/3 = 1/4x + 7 (get all x terms on one side)
7/4x+4/3-1/4x=1/4x+7-1/4x
6/4x+4/3=7 (add additive inverse of 4/3 to both sides)
6/4x+4/3-4/3=7-4/3
6/4x=17/3 (divide both sides by 6/4 to leave x alone)
x= (17/3)/(6/4)
x=34/9
8t-4/5 + 9t-2/2=47
I understand this question as: (8t-4)/5 + (9t-2)/2=47
To get rid of those fractions, multiply both sides by the LCD of 10;
10.((8t-4)/5 + (9t-2)/2 )= 10.47
10.(8t-4)/5 + 10.(9t-2)/2 =470
2.(8t-4)+5.(9t-2)=470 ( by using distriutive property we remove the parantheses )
16t-8+45t-10=470
61t-18=470 (add additive inverse of -18 to both sides)
61t-18+18=470+18
61t=488 (divide both sides 61)
61t/61=488/61
t=8

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