Question
Is 2x+3y^2 > 25 an linear inequality
Answers
GPT-4o mini
The inequality \(2x + 3y^2 > 25\) is not a linear inequality.
In a linear inequality, both variables (in this case \(x\) and \(y\)) should have a degree of 1. However, in this inequality, the term \(3y^2\) involves \(y\) raised to the power of 2, making it a quadratic expression in \(y\). Thus, the presence of the \(y^2\) term means that the inequality is nonlinear.
In summary, \(2x + 3y^2 > 25\) is a nonlinear inequality due to the quadratic term \(3y^2\).
In a linear inequality, both variables (in this case \(x\) and \(y\)) should have a degree of 1. However, in this inequality, the term \(3y^2\) involves \(y\) raised to the power of 2, making it a quadratic expression in \(y\). Thus, the presence of the \(y^2\) term means that the inequality is nonlinear.
In summary, \(2x + 3y^2 > 25\) is a nonlinear inequality due to the quadratic term \(3y^2\).