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Solve each inequality. See Example 3.$$(4-3 x)^{2} \geq-2$$
$$(-\infty, \infty)$$
Precalculus
Algebra
Chapter 11
Quadratic Equations, Inequalities, and Functions
Section 8
Polynomial and Rational Inequalities
Introduction to Conic Sections
Equations and Inequalities
Functions
Polynomials
McMaster University
Harvey Mudd College
Idaho State University
Lectures
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all right we have in this exercise. Four minus three acts squared is greater than or equal. It's a negative, too. Now, here's a trick to this one, and we can save ourselves a lot of work if we can recognize what's going on here. Now, notice that this four ministry acts is being squared and because we're squaring it and whenever you square a number, if you square a positive number, it would be positive if you square a negative number. Brain three squared is nine negative. Three squared is nine, right? So whenever we square a negative number, we get a positive number, so the left side will always be positive. Therefore, if it's always positive, it has to always be greater than or equal to negative two. So this is always gonna be true, no matter what value I pick cracks. So, in other words, the solution said, it's simply going to be the satin of all real numbers or, in other words, the interval from negative infinity. It a positive infinity because we're squaring this expression. It always has to be true
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