2| x - 3 | > 8, 2| x - 3 | < -8 Sovle the inequality involving absolute value? I don't understand how to get the right answer

Answers

Answer 1

Answer: divide both sides by 2

|x-3|>4 and |x-3|<-4
ok so |x-3|<-4 is false, since |x|≥0 always

so we have
|x-3|>4
now assume
x-3>4 and
x-3<-4

x-3>
add 3
x>7

x-3<-4
add 3
x<-1

so
-1>x and x>7

so basically it is all numbers from -∞ to +∞ except from -1 to 7
in interval notaion
(-∞,-1)U(7,∞)

S={x|x<-1 or x>7}

Answer 2

Answer: X >7 and X > -1 that would be the answer

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What values of x will make x^2 = 16 true ?

Answers

Answer:

x = 4, x = -4

Step-by-step explanation:

In order to solve this equation, we need to square-root bothsides.

$\sf{x^2=16}$

$√(x^2)=√(16)$

Simplify:

$x=4,x=-4$

Answer:

x = -4 or 4

Step-by-step explanation:

⇒ $x^2=16$

⇒ $x = √(16)$

∴ $x =$ ± 4

Therefore, x can be either 4 or -4 such that $x^2=16$ .

Thank You :)

Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

Answers

It looks like we have

$f(x)=\begin{cases}5-x&\text{for }x<5\n8&\text{for }x=5\nx+3&\text{for }x>5\end{cases}$

and we want to find $\lim\limits_(x\to5)f(x)$ .

Since $x$ is approaching 5, we don't care about the value of $f(x)$ when $x=5$ .

We do care about how $f(x)$ behaves to either side of $x=5$ . If $x\to5$ from below, then $f(x)=5-x$ , so that

$\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)(5-x)=5-5=0$

On the other hand, if $x\to5$ from above, then $f(x)=x+3$ , so that

$\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)(x+3)=5+3=8$

The one-sided limits do not match, since 0 ≠ 8, so the limit does not exist.

solve by substitution ( show steps)

y=3x+2

3x-y=2

Answers

$\left\{\begin{array}{ccc}y=3x+2\n3x-y=2\end{array}\right\n\nsubstitute\n\n3x-(3x+2)=2\n3x-3x-2=2\n-2=2-FALSE\n\nAnswer:No\ solution$

$y=3x+2\n 3x-y=2\n\n 3x-(3x+2)=2\n 3x-3x-2=2\n -2=2\n x\in\emptyset \Rightarrow y\in\emptyset$

How do i find the answer to this problem? 2/6 x 24 = m working with fractions

Answers

Solve for m by simplifying both side of the equation,then isolating the variable.

M=8
Hope that this helps :)

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Answers

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Answers

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