Write a compare piecewise function and step function

Solve absolute value inequality.
${\displaystyle |x-1|\le 2}$

Cauchy inequalities in systems of equations
For positive real numbers solve the system of equations
$\{\begin{array}{l}\begin{array}{r}{x}_1+x_2+···+x_n=\frac{1}{4}\\ \frac{1}{x_1}+\frac{4}{x_2}+···+\frac{n^2}{x_n}=n^2(n+1{)}^2\end{array}\end{array}$

The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer $x_1$ (in $1000) and on the square footage of the home $x_2(\text{ in }100f{t}^2)$ according to $y=a{x}_1+b{x}_2+c$
The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. a) Use the data to write a system of linear equations to solve for a, b, and c.
b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.
c) Write the model $y=a{x}_1+b{x}_2+c$
d) Predict the purchase price for a buyer who makes $100000 per year and wants a $2500f{t}^2$ home.

Calculate the quadratic irrational number $\alpha$ given by the periodic continued fraction $\alpha =\overline{[1,2,1]}$.

Describe all numbers x that are at a distance of 4 from the number 6. Express this using absolute value notation.

Find the points on the curve ${\displaystyle y=2x^3+3x^2-12x+1}$ where the tangent is horizontal.

To simplify: The given expression.
${\displaystyle {\left(x^{14}\right)}^{23}}$