True or false:
a. |3x-5|=|2x+4| if and only if 3x-5=2x+4 or 3x-5= -(2x+4) ______
b. |2x+7|=-4 if and only if 2x+7=4 or 2x+7=-4 ______
how do you do these and what's the answer?
thanks
b. How can abs () ever be negative?
a. Isn't that the definition of what happens in an abs function?
but is it true or false?
The abs are || and the () are parantheses
You have to do your own thinking. I gave you the answer. If something is the definition, it must be true.
Online, absolute function is written abs(xxxx) where xxxx is the argument.
Wasn't this a summer assignment, due in the upcoming week?
To determine whether the given statements are true or false, we need to understand the properties of absolute value and how to solve equations involving absolute values. Let's break it down step by step:
a. |3x-5|=|2x+4|
To simplify, we remove the absolute value signs and create two separate equations:
1. If 3x-5 is positive:
3x-5 = 2x+4
2. If 3x-5 is negative:
3x-5 = -(2x+4)
Now we can solve each equation:
1. If 3x-5 is positive:
Subtract 2x from both sides:
x - 5 = 4
Add 5 to both sides:
x = 9
2. If 3x-5 is negative:
Distribute the negative sign:
3x-5 = -2x-4
Add 2x to both sides:
5x-5 = -4
Add 5 to both sides:
5x = 1
Divide by 5:
x = 1/5
So, the solutions to the equation |3x-5|=|2x+4| are x = 9 and x = 1/5.
Therefore, the statement is true: |3x-5|=|2x+4| if and only if 3x-5=2x+4 or 3x-5=-(2x+4).
b. |2x+7| = -4
The absolute value of any real number is always greater than or equal to zero. It cannot be negative. Therefore, there are no solutions to this equation.
So, the statement is false: |2x+7| = -4 cannot be true since the absolute value cannot be negative.
In summary:
a. True |3x-5|=|2x+4| if and only if 3x-5=2x+4 or 3x-5=-(2x+4).
b. False |2x+7| = -4.