problem #1
(1+x)/(2x+3)<1 algebraically
problem #2
1/(x^2+2x+1) > 2 graphically
TIA
please ignore this
No problem! I'd be happy to help you with your questions.
Problem #1:
To solve the inequality (1+x)/(2x+3) < 1 algebraically, we can follow these steps:
1. Start by multiplying both sides of the inequality by (2x+3) to eliminate the denominator:
(1+x) < (2x+3)
2. Expand the equation:
1 + x < 2x + 3
3. Collect like terms:
x - 2x < 3 - 1
-x < 2
4. Divide both sides by -1, but remember that when dividing by a negative number, the inequality sign flips:
x > -2
Therefore, the solution to the inequality is x > -2.
Problem #2:
To determine the solution to the inequality 1/(x^2+2x+1) > 2 graphically, we can plot the graph of the function f(x) = 1/(x^2+2x+1) and identify the regions where f(x) is greater than 2:
1. First, rewrite the inequality in terms of the function f(x):
f(x) = 1/(x^2+2x+1)
f(x) > 2
2. Graph the function f(x) = 1/(x^2+2x+1) on a coordinate plane.
The graph might show that the function f(x) is positive or negative in different regions.
3. Identify the regions where f(x) is greater than 2 on the graph.
These regions will correspond to the values of x for which the inequality 1/(x^2+2x+1) > 2 holds true.
Please note that solving inequalities graphically can provide an approximate solution, but it's always a good idea to verify the solution algebraically as well.
I hope that helps! Let me know if you have any further questions.