I have a couple questions, I need to know how to solve these type of problems.
X^2 -4< X + 16
5/n+2 - 5/n = 2/3n
2X^3-x^2-6X + 1/ X^2 + 5x - 8
1) rearragne the terms to get
x^2-x-20<0
(x-5)(x+4)<0
which means that one term can be negative, or -4<x<5 check that.
2) multipy both sides by n(n+2) rearrange terms to see if you can factor and solve as in the first.
3) Is not an equation. It is just an algebraic expression. There is nothng to solve. Did you omit an = sign?
To solve the problem X^2 - 4 < X + 16:
Step 1: Rearrange the terms to one side of the inequality:
X^2 - X - 20 < 0
Step 2: Factor the quadratic expression:
(X - 5)(X + 4) < 0
Step 3: Determine the sign of each factor:
(X - 5) < 0 and (X + 4) < 0
Step 4: Solve each equation separately:
X - 5 < 0 --> X < 5
X + 4 < 0 --> X < -4
Step 5: Determine the values of X that satisfy the original inequality:
-4 < X < 5
Therefore, the solution to X^2 - 4 < X + 16 is -4 < X < 5.
To solve the problem 5/n+2 - 5/n = 2/3n:
Step 1: Multiply both sides of the equation by the common denominator, which is n(n+2) and simplify:
(5)(n) - (5)(n+2) = (2)(n)(n+2)/(3)(n)
Step 2: Simplify the equation by distributing and combining like terms:
5n - 5n - 10 = 2n(n+2)/3n
Step 3: Simplify further:
-10 = 2(n+2)/3
Step 4: Multiply both sides of the equation by 3 to eliminate the denominator:
-30 = 2(n+2)
Step 5: Distribute and solve for n:
-30 = 2n + 4
-34 = 2n
n = -17
Therefore, the solution to 5/n+2 - 5/n = 2/3n is n = -17.
Regarding the third problem, "2X^3-x^2-6X + 1/ X^2 + 5x - 8", it seems to be an algebraic expression rather than an equation, as there is no equal sign. If you meant to include an equal sign, please provide the complete equation so that it can be solved.