Question

Which statements are true? Check all that apply.

Answer 1

The equation |–x – 4| = 8 will have two solutions.
The equation 3.4|0.5x – 42.1| = –20.6 will have one solution.
The equation StartAbsoluteValue StartFraction one-half EndFraction x minus StartFraction 3 Over 4 EndFraction EndAbsoluteValue equals 0. = 0 will have no solutions.
The equation |2x – 10| = –20 will have two solutions.
The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.
The equation StartAbsoluteValue StartFraction 1 Over 8 EndFraction x minus 1. EndAbsoluteValue equals 5. = 5 will have infinitely many solutions.

Answer 2

Ok well, For option one,
\[|−x−4|=8\]
Find the absolute value with
\[−x−4=8\ or−x−4=−8\]\[−x−4=8\]
+4 to both sides
\[−x−4+4=8+4\]\[−x=12\]
÷ by -1 to both of the sides
\(\LARGE\frac{-x}{-1}=\frac{12}{-1}\)
So, \[x=−12
\]
Or,
\[−x−4=−8\]
+4 to both sides\[−x−4+4=−8+4\]\[−x=−4\]
÷-1, both sides
\(\frac{-x}{-1}=\frac{-4}{-1}\)\[x=4\]
So yes, there is two solutions, \(x=−12\ and\ x=4\)

Answer 3

Option two,
\[3.4(|0.5x−42.1|)=−20.6\]
÷3.4, both sides
\(\LARGE\frac{3.4(|0.5x−42.1|)}{3.}=\frac{−20.6}{3.4}\)\[|0.5x−42.1|=−6.058824
\]
Absolute value: \[|0.5x−42.1|=−6.058824\]
Meaning that there is \(No~solution\)

Answer 4

Ok, and how are you helping?

Answer 5

I already knew that I `got it` and you just came saying something that doesn't help at all.

That is spam, low-effort replies to raise your SmartScore.
```
-No serious attempt to help
-Low-effort reply
-Spam

Answer 6

I know you got your solution already but there will only be 3 types of solutions: No solution many or one. with no solution they will never intersect ever but with many they will intersect forever and with one solution they will only intersect once.

Answer 7

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Timmyspu
I know you got your solution already but there will only be 3 types of solutions: No solution many or one. with no solution they will never intersect ever but with many they will intersect forever and with one solution they will only intersect once.
\(\color{#0cbb34}{\text{End of Quote}}\)
And how does this help?

Answer 8

Option one, yes, option 2, no
Now for option 3,
\(\LARGE|\frac{1}{2}x−\frac{3}{4}|=0\)

Absolute value,
\(\LARGE\frac{1}{2}x+\frac{−3}{4}=0\)

+\(\frac{3}{4}\), both sides
\(\LARGE\frac{1}{2}x+\frac{−3}{4}+\frac{3}{4}=0+\frac{3}{4}\)

\(\LARGE\frac{1}{2}x=\frac{3}{4}\)
(2), both sides,
\(\LARGE2*(\frac{1}{2}x)=2*(\frac{3}{4})\)

\(\LARGE\ x=\frac{3}{2}\)
So this does have a solution.
Option 3 is incorrect.

Answer 9

Option 4,
it's less than 0 meaning that this has \(No\ solutions\)
So option 4 is incorrect.

Answer 10

Option 5,
\[|0.5x−0.75|+4.6=0.25\]
+-4.6, both sides
\[|0.5x−0.75|+4.6+−4.6=0.25+−4.6\]\[|0.5x−0.75|=−4.35\]
Absolute value, \[|0.5x−0.75|=−4.35\] less than 0, no solution, option 5 is correct/true

Answer 11

Option 6,
\(\LARGE|\frac{1}{8}x−1|=5\)
Positive 5 or negative 5
\(\LARGE\frac{1}{8}x−1=5\)
+1, both sides
\(\LARGE\frac{1}{8}x−1+1=5+1\)

\(\LARGE\frac{1}{8}x=6\)
*8, both sides
\(\LARGE 8*(\frac{1}{8}x)=(8)*(6)\)\[x=48\]
Or
\(\LARGE\frac{1}{8}x−1=−5\)

\(\LARGE\frac{1}{8}x−1+1=−5+1\)
\(\LARGE\frac{1}{8}x=−4\)
*8, both sides
\(\LARGE 8*(\frac{1}{8}x)=(8)*(−4)\)
\[x=−32\]
So we have \[x=-32\ and\ x=48\]