Question 344402: I desperately need help with a math problem. I've done it several different times, but every time I enter the answer I get, the program I do my homework on says it's wrong.
1 + |9t -6| = 5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Equation is:
1 + abs(9T-6) = 5
Subtract 1 from both sides of this equation to get:
abs(9T-6) = 4
If abs(x) = y, this means that x = y if x is positive, and -x = y if x is negative.
In your equation, 9T-6 is equal to x, and 4 is equal to y.
You get:
9T-6 = 4 when (9T-6) is positive.
You get:
-(9T-6) = 4 when (9T-6) is negative.
Solve the equation for when T is positive.
You get 9T-6 = 4
Add 6 to both sides of this equation to get 9T = 10
Divide both sides of this equation by 9 to get T = (10/9).
Solve the equation for when T is negative.
You get -(9T-6) = 4
Remove parentheses to get -9T + 6 = 4
Subtract 6 from both sides of this equation to get -9T = -2
Divide both sides of this equation by -9 to get T = (2/9).
Your answer is that T can be either (10/9) or (2/9).
Substitute in your original equation to see if this is true.
Your original equation is 1 + abs(9T-6) = 5
Subtract 1 from both sides of this equation to get:
abs(9T-6) = 4.
Substitute (10/9) for T to get:
abs(9*(10/9)-6) = 4 which becomes:
abs(10-6) = 4 which becomes:
abs(4) = 4 which becomes:
4 = 4 which is true, so the answer of T = (10/9) is good.
Substitute (2/9) for T to get:
abs(9*(2/9)-6) = 4 which becomes:
abs(2-6) = 4 which becomes:
abs(-4) = 4 which becomes:
4 = 4 which is true, so the anser of T = (2/9) is good.
Let me know if these are the correct answers.
I believe that they are.
The main thing you do when solving absolute equation is to solve for when the expression is positive and to solve for when the expression is negative.
abs(expression) = answer becomes expression = answer when expression is positive.
abs(expression) = answer becomes - expression = answer when expression is negative.
The expression in your case was (9T-6).
If (x) is the expression, and y is the answer, then the equation becomes:
abs(x) = y if and only if:
x = y when x is positive.
-x = y when x is negative.
You will also see a rule that states:
abs(x) = y if and only if:
x = y when x is positive.
x = -y when x is negative.
This rule is derived from what I originally stated.
if -x = y, then multiply both sides of the equation by -1 to get x = -y.
That's what leads to the alternate form of the solution to the absolute value of equation.
It becomes more fun when you get to inequalities as you will see soon enough, if not already.
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