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Inequality

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Solve the inequality (4-z)(z+7) ≥ 2

Jun 17, 2022

#2
+117758
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You might find it easier if you swap the z for an x and the swap it back at the end

$$(4-z)(z+7) ≥ 2\\ (4-x)(x+7) ≥ 2\\ -x^2 -3x +28 \ge 2\\ -x^2 -3x +26 \ge 0\\ x^2+3x -26 \le 0\\$$

$$y=x^2+3x-26\\ \text{Is a concave up parabola}$$

So it will be less than 0 between the roots.  Draw it to see what i mean

Use the quadratic formula to find the roots

etc

Jun 18, 2022