Exercise
Solve the inequality:
Final Answer
Solution
Open brackets:
Move everything to one side:
It is a square inequality. Its coefficients are
The coefficient of the square expression (a) is positive, so the parabola (quadratic equation graph) “smiles” (= bowl-shaped). The sign of the inequality means we are looking for the sections the parabola is above the x-axis. We find the solutions (= zeros = roots) of the quadratic equation using the quadratic formula. Putting the coefficients in the formula gives us
Hence, the factorizing of the equation is
Hence, we receive that our inequality equals
The left side is a squared phrase and therefore is always greater than zero except at a point where it is zero. Let’s see when it’s equal to zero:
Therefore, the inequality is true for all x except this point.
In other words, inequality solution is
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