Question 23035
1.  3/4(24-20t) + 9t = 2(5t+1)

Remember the distributive property?  It works really well here.  Take 3/4 of 24, which is 18 and 3/4 of 20t, which is 15t.  Can you do that?


3/4(24-20t) + 9t = 2(5t+1)
18 -15t + 9t = 10t + 2


Combine like terms:
18 - 6t = 10t + 2


Get all the t terms on one side, maybe by adding 6t to each side:
18 - 6t + 6t = 10t + 6t + 2
18 = 16t + 2


Now get all the number terms on the other side (the left side) by subtracting 2 from each side:
18-2 = 16t + 2 - 2
16 = 16t


Divide both sides by 16:

{{{16/16 = 16t/16}}}
{{{1=t}}}


Check by substituting t=1:
3/4(24-20t) + 9t = 2(5t+1)
3/4(24-20) + 9 = 2(5+1)
3/4(4) + 9= 2(6)
3+9=12
12=12 It checks!!


2.  7(b+2)-4b=2(b+10)
Distributive property again:
   7b + 14 - 4b = 2b + 20
3b + 14 = 2b + 20


Subtract 2b from each side to get variables all on the left side:
3b - 2b + 14 = 2b - 2b + 20
b+ 14 = 20


Subtract 14 from each side to get all number terms on the right:
b+14 - 14= 20 - 14
b= 6


Check by substituting b=6:
7(b+2)-4b=2(b+10)
7(6+2) -4*6= 2(6+10)
7(8)-24= 2(16)
56-24 = 32
32=32  It checks!!


3. 2(6-2x)= -9x-1/2(-4x+6)
   12 - 4x = -9x + 2x - 3
  12 - 4x = -7x - 3


Add +7x to each side to get the variables on the left side:
12-4x + 7x = -7x + 7x - 3
12 + 3x = -3


Subtract 12 from each side to get the variables on the right side:
12-12 + 3x = -3 -12
3x = -15


Divide both sides by 3:

{{{3x/3 = -15/3}}}
{{{x=-5}}}


Check:By substituting x= -5  (This one might be harder to check than it was to solve!):
2(6-2x)= -9x-1/2(-4x+6)
2(6-2*-5)= -9*-5 -1/2(-4*-5+6)
2(6+10)= 45 -1/2(20+6)
2(16) = 45 -1/2(26)
32 = 45 - 13
32= 32  It checks!!


I remember when I was in the 8th grade!  Abraham Lincoln was the President!!


R^2 at SCC


P.S.  See my lesson plan on Basic Equation Solving in the Equations topic of algebra.com!!