SOLUTION: Solve the equation and check the solution? 4(5z-1)-3(z+6)=10(z+1)

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Question 631564: Solve the equation and check the solution?
4(5z-1)-3(z+6)=10(z+1)
Found 2 solutions by jim_thompson5910, lenny460:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%285z-1%29-3%28z%2B6%29=10%28z%2B1%29 Start with the given equation.


20z-4-3z-18=10z%2B10 Distribute.


-22%2B17z=10z%2B10 Combine like terms on the left side.


17z=10z%2B10%2B22 Add 22 to both sides.


17z-10z=10%2B22 Subtract 10z from both sides.


7z=10%2B22 Combine like terms on the left side.


7z=32 Combine like terms on the right side.


z=%2832%29%2F%287%29 Divide both sides by 7 to isolate z.


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Answer:

So the solution is z=32%2F7

To perform the check, you plug the solution back into the given equation. Then you simplify. If you get a true equation, then the solution is verified.

I'll let you do the check.


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Answer by lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation and check the solution?
4(5z-1)-3(z+6)=10(z+1)
Multiply:
4 * 5z = 20z
4 * -1 = -4
-3 * z = -3z
-3 * 6 = -18
10 * z = 10z
10 * 1 = 10
Therefore:
20z - 4 - 3z - 18 = 10z + 10
Combine like terms:
20z - 3z = 17z
-4 - 18 = -22
We now have:
17z - 22 = 10z + 10
Subtract 10z from each side of the equation.
17z - 22 - 10z = 10z + 10 - 10z
Combine like terms:
17z - 10z = 7z
10z - 10z = 0
Therefore:
7z - 22 = 10
Add 22 to each side of the equation.
7z - 22 + 22 = 10 + 22
Combine like terms:
-22 + 22 = 0
10 + 22 = 32
We now have:
7z = 32
Divide each side by 7
7z/7 = 32/7

The Answer:
z = 32/7


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