SOLUTION: i need help on solving linear equations can anyone help me? 1. 3/4(24-20t)+9t=2(5t+1) 2. 7(b+2)-4b=2(b+10) 3. 2(6-2x)= -9x-1/2(-4x+6)

Question 23035: i need help on solving linear equations can anyone help me?

1. 3/4(24-20t)+9t=2(5t+1)
2. 7(b+2)-4b=2(b+10)
3. 2(6-2x)= -9x-1/2(-4x+6)
thank you
ps. im in 8th grade
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
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:

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:

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!!

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