SOLUTION: I need to understand how to break this question: Two thirds of a number reduced by 11 is equal to 4 more than the number. Find that number. I need to know how to break this probl

Question 111524: I need to understand how to break this question:
Two thirds of a number reduced by 11 is equal to 4 more than the number. Find that number. I need to know how to break this problem in order to solve it.
question 2:
Also, I need help with this question:
Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number. What is the number?
question 3: 1/2 (6-Z)=Z
Question 4: 2 (a-8)=7=5(a+2)-3a-19.
Thank you for in advance.
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
2X/3-11=X+4
2X/3-X=11+4
2X/3-X=15
(2X-3X)/3=15
-X/3=15 CROSS MULTIPLY.
-X=45
X=-45 ANSWER.
PROOF
2*-45/3-11=-45+4
-90/3-11=-41
-30-11=-41
-41=-41

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Start by assigning a variable to the number you want to find. Let's call it n. Now let's write an expression for the relationship that was described.
:
First, we need an expression for two thirds of the number. This is simply .
:
Then we need to reduce that amount by 11. That gives us .
:
Four more than the number is just . And finally, the problem tells us that these two quantities are equal, so:
:

:
All that is left is to solve the equation for n:
:
Add -4 to both sides:

:
Add -(2/3)n to both sides:

:
Combine terms:

:
Multiply both sides by 3:
:

:
Last step -- VERY IMPORTANT -- Check your answer.
:
Two thirds of -45 is -30, reduced by 11 is -30 - 11=-41
Four more than -45 is -45 + 4 = -41
:
The answer checks!
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