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Solve the inequality (4-z)(z+7) ≥ 2

 Jun 17, 2022
 #2
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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

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