Raerin said:Solve the inequality 12x^3 + 8x^2 ≤ 3x + 2 and justify your answer.
To justify the answer do you need to make a sin chart and graph it?
Oops, I made a typo, so yes, I do mean sign chart.I like Serena said:Hi Raerin! :)
The usual approach is to first solve the equality.
Then take the derivative and find its roots.
Then you can make a sign chart to read off the solution (did you mean a sign chart instead of a sin chart?)
The first step is already not so easy for this particular problem.
As Petrus suggested, the easiest way to find the roots is by using the Rational root theorem.
Do you know of it?
Raerin said:Oops, I made a typo, so yes, I do mean sign chart.
You're supposed to bring everything to one side, right? Then you find the number that would make the polynomial = 0?
An inequality is a mathematical statement that compares two quantities, expressing that one quantity is greater than, less than, or not equal to the other.
To solve an inequality, you must isolate the variable on one side of the inequality sign and perform the same operation on both sides of the inequality until the variable is alone.
The main difference between solving an equation and solving an inequality is that equations have an equal sign, while inequalities have a greater than, less than, or not equal to sign. Inequalities also have a range of possible solutions, while equations typically have only one solution.
Justifying the solution of an inequality is important because it ensures that the solution is accurate and valid. It also helps to explain the reasoning behind the solution and provides evidence to support the answer.
Some common mistakes when solving inequalities include forgetting to reverse the inequality symbol when multiplying or dividing by a negative number, incorrectly distributing a negative sign, and forgetting to switch the direction of the inequality when dividing by a negative number.