Find the value of x that satisfies the inequality.|x-5|<9

If y varies directly as x, and y = 9 when x = 2, what is y when x = -3?

How do you find ${\displaystyle (f\cdot g)\left(x\right)}$ and ${\displaystyle (g\cdot f)\left(x\right)}$ and determine if the given functions are inverses of each other ${\displaystyle f\left(x\right)=x^2-3}$ and ${\displaystyle g\left(x\right)=\sqrt{x}+3}$?

An inequality constraint problem
${\displaystyle min\frac{1}{2}{(x_1-1)}^2+\frac{1}{2}{(x_2-2)}^2}$
s.t. ${\displaystyle x_1-x_2=1\text{and}{x}_1+x_2\le 2}$

Correct me if I am wrong. Find the value(s) of the constant k such that the system of linear equations
$\{\begin{array}{l}x+2y=1\\ k^{2}x-2ky=k+2\end{array}$
has:
1. No solution
2. An infinite number of solutions
3. Exactly one solution
Answer:
so the first step is to get row reduction form, which is:
from $\left[\begin{array}{cc}1& 2\\ k^2& -2k\end{array}\right]$,
to $\left[\begin{array}{cc}1& 2\\ 0& -2k+2k^2\end{array}\right]$

Range of x for which the modulus inequality will be valid: ${\displaystyle |x^2-2x-8|>2x}$: Need clarification about solution set

The ${\displaystyle x^2+ax+b=0}$ has only one solution and this is ${\displaystyle x=-1+\frac{1}{2}}$. What are the values of a and b?

Use the quadratic formula ${\displaystyle y^2-7y-5=0}$