Chapter 4: Q. 2 (page 247)

Solve the inequality $x^{2} \geq x$ and graph the solution set.

Short Answer

Expert verified

The solution set of inequality is $[- \infty, 0] \cup [1, \infty]$

Step by step solution

Step 1. Given Information

The given inequality is $x^{2} \geq x$

Step 2. Calculation

Solve the inequality by rearranging it such that the right side has 0.

$x^{2} - x \geq 0 x (x - 1) \geq 0$

To determine the real zero, substitute the function equal to zero.

$x (x - 1) = 0 x = 0 o r x - 1 = 0 \Rightarrow x = 1$

Thus, the real number line can be divided into three intervals as follows,

Thus, the solution set of the inequality is $[- \infty, 0] \cup [1, \infty]$

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Solve the inequality $x^{2} \geq x$ and graph the solution set.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Short Answer

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Solve the inequality $x^{2} \geq x$ and graph the solution set.