# 5.6.28 find domain of x in ABS

• MHB
• karush
In summary: The summary of the conversation is that the problem is to find the value of $x$ when $|2x-5|<9$, and it can be divided into two solution sets. The answer is $-2<x<7$ and there is a discussion about notation and the use of $\in$ versus \quad. In summary, the conversation is about finding the value of $x$ when $|2x-5|<9$ and discussing notation and spacing options for writing the equation.
karush
Gold Member
MHB
$\tiny{\textit{5.6.28}}$
Find $x \quad |2x-5|<9$
divide into 2 solution sets
$\begin{array}{rl|rl} (2x-5)&=9&-(2x-5)&=9 \\ 2x&=14&-2x&=4 \\ x&=7&x&=-2 \end{array}$
x is $-2<x<7$
kinda maybe...

Last edited:
karush said:
Find x \quad $|2x-5|<9$

-Dan

topsquark said:

-Dan
oh its a latex H space A \quad B is $A \quad B$

karush said:
oh its a latex H space A \quad B is $A \quad B$
I'm not seeing anything between A and B. Just go ahead and write it as: Find all x such that |2x - 5| < 9. Or Find all x s.t. |2x - 5| < 9.

You answer looks good to me. Why are you not sure it's right?

-Dan

Wait. Are you trying to write $$\displaystyle x \in |2x - 5| < 9$$? You are looking for a lower case epsilon. But you can simply write it as \in.

If this is the case your notation doesn't really work all that well. Just go ahead and write it like I suggested above.

-Dan

Last edited by a moderator:
well actually when you start the question with "Find x" sometime the x looks it is part of the equation therefore it needs to separated from it,,,, \quad is often used to do this... just markup stuff...

 Find x $\quad |2x-5|<9$

using $\in$ in an algebra class might knock some students off the saddle

karush said:
well actually when you start the question with "Find x" sometime the x looks it is part of the equation therefore it needs to separated from it,,,, \quad is often used to do this... just markup stuff...

 Find x $\quad |2x-5|<9$

using $\in$ in an algebra class might knock some students off the saddle
Oh! I see. I just use ~ for my spacer.

I was introduced to $$\displaystyle \in$$ in 7th grade. But it averages itself out... there was also a bunch of stuff they didn't do either.

-Dan

i was in the 7th grade in 1957 it was a dense class

## 1. What is the meaning of "5.6.28 find domain of x in ABS"?

"5.6.28 find domain of x in ABS" is a mathematical expression that is asking for the domain, or set of possible input values, for a function that involves the absolute value of x.

## 2. How do you find the domain of x in an absolute value function?

To find the domain of x in an absolute value function, set the expression inside the absolute value bars equal to 0 and solve for x. This will give you the value or values that cannot be included in the domain. Then, write the domain in interval notation, using parentheses for excluded values and brackets for included values.

## 3. What are some common mistakes when finding the domain of x in an absolute value function?

One common mistake is forgetting to include the excluded values in the domain. Another mistake is incorrectly solving for x and not considering both positive and negative solutions. It is also important to check for any other restrictions, such as a denominator that cannot equal 0.

## 4. Can the domain of x in an absolute value function ever be all real numbers?

No, the domain of x in an absolute value function can never be all real numbers. Absolute value functions have a V-shaped graph, and the domain will always be limited by the x-values where the graph changes direction.

## 5. How does the domain of x in an absolute value function affect the graph of the function?

The domain of x in an absolute value function determines the range of x-values that will be included in the graph. If the domain is limited, the graph will be a portion of the V-shape. If the domain is all real numbers, the graph will be a complete V-shape.

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