Unit Name: Polynomial and Rational Functions Solve the following inequality algebraically. Explain your process. 8x−3≤2x+1≤17x−8

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Unit Name: Polynomial and Rational Functions   Solve the following inequality algebraically. Explain your process.   8x−3≤2x+1≤17x−8

Karen Robbins · Accepted Answer

Split the inequality into two:   8x−3≤2x+1 and 2x+1≤17x−8   Isolate x from each inequality using inverse operations.   8x−3≤2x+1   8x−2x≤3+1   6x≤4   x≤23   AND   2x+1≤17x−8   2x−17x≤−8−1   −15x+15x≤−9+15x   0≤−9+15x   35≤x  Therefore, the solution is: 35≤x≤23

Shannon Hodgkinson · Accepted Answer

Solve the following inequality algebraically.Explain your process.8x−3≤2x+1≤17x−8We&#039;ve 8x−3≤2x+1≤17x−8. (1)⇒8x−3−1≤2x+1−1≤17x−8−1⇒8x−4≤2x≤17x−9Now dividing above equation by 2 we get⇒8x−42≤2x2≤172x−92⇒4x−2≤x≤172x−92 (2)Now from equation (2) we&#039;ve two cases.(1) x≥4x−2⇒ adding 2 to both sides we get⇒x+2≥4x−2+2⇒x+2≥4xSubtracting x from both sides⇒x+2−x≥4x−x⇒2≥3x⇒x≤23x≤172x−92adding 92 to both sides we get⇒x+92≤172x−92+92⇒x+92≤172xSubtracting x from both sides⇒x+92−x≤172x−x⇒q2≤17x−2x2⇒92≤15x2Multiplying 2 to both sides we getUndefined control sequence cancelUndefined control sequence cancel⇒9≤15x⇒x≥35 (4)From equation (3) and equation (4) we get35≤x≤23⇒0.6≤x≤0.6666

Unit Name: Polynomial and Rational Functions Solve the following inequality algebraically.

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