killjoy1990xb9

2021-12-15

Solve absolute value inequality.

$|x-1|\ge 2$

scoollato7o

Beginner2021-12-16Added 26 answers

Step 1

the given inequality is:

$|x-1|\ge 2$

we have to solve the given inequality.

Step 2

the given inequality is$|x-1|\ge 2$

as we know that if$\left|x\right|\ge a$

then$x\le -a\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}x\ge a$

that implies$x\in (-\mathrm{\infty},-a]\cup [a,\mathrm{\infty})$

therefore,

$|x-1|\ge 2$

then

$x-1\le -2\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}x-1\ge 2$

$x-1\le -2$

$x\le -2+1$

$x\le -1$

or

$x-1\ge 2$

$x\ge 2+1$

$x\ge 3$

Step 3

therefore the solution of the given inequality is$x\le -1\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}x\ge 3$

that implies the solution of the given inequality is$x\in (-\mathrm{\infty},-1]\cup [3,\mathrm{\infty})$

the given inequality is:

we have to solve the given inequality.

Step 2

the given inequality is

as we know that if

then

that implies

therefore,

then

or

Step 3

therefore the solution of the given inequality is

that implies the solution of the given inequality is

Donald Cheek

Beginner2021-12-17Added 41 answers

Step 1

The absolute value inequality is given as,

$|x-1|\ge 2$

If an absolute inequality is given as,$\left|f\left(x\right)\right|\ge a$ ,

$\left|f\left(x\right)\right|\ge a$

$$=\{\begin{array}{ll}f(x)\ge a& f(x)>0\\ f(x)\le -a& f(x)<0\end{array}$$

Step 2

On solving the inequality, we get

$x-1\ge 2$

$x\ge 2+1$

$x\ge 3$ ...(i)

And,

$x-1\le -2$

$x\le -2+1$

$x\le -1$ ...(ii)

Therefore, the interval for the solution of the given inequality is$x\in (-\mathrm{\infty},-1]\cup [3,\mathrm{\infty})$

The absolute value inequality is given as,

If an absolute inequality is given as,

Step 2

On solving the inequality, we get

And,

Therefore, the interval for the solution of the given inequality is

Find the volume V of the described solid S

A cap of a sphere with radius r and height h.

V=??

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

?

$d)f\left(x\right)={x}^{5}+1$In how many different orders can five runners finish a race if no ties are allowed???

State which of the following are linear functions?

a.$f(x)=3$

b.$g(x)=5-2x$

c.$h\left(x\right)=\frac{2}{x}+3$

d.$t(x)=5(x-2)$ Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

A square is also a

A)Rhombus;

B)Parallelogram;

C)Kite;

D)none of theseWhat is the order of the numbers from least to greatest.

$A=1.5\times {10}^{3}$,

$B=1.4\times {10}^{-1}$,

$C=2\times {10}^{3}$,

$D=1.4\times {10}^{-2}$Write the numerical value of $1.75\times {10}^{-3}$

Solve for y. 2y - 3 = 9

A)5;

B)4;

C)6;

D)3How to graph $y=\frac{1}{2}x-1$?

How to graph $y=2x+1$ using a table?

simplify $\sqrt{257}$

How to find the vertex of the parabola by completing the square ${x}^{2}-6x+8=y$?

There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?

Write 18 thousand in scientific notation.