How do you solve #5x ( 3x - 2) + 2( 14- 5x ) > 2( 2x + 5) - 5#?

1 Answer
Douglas K.
Nov 5, 2017

Given: #5x ( 3x - 2) + 2( 14- 5x ) > 2( 2x + 5) - 5#

Perform the implied multiplication on all of the terms with parenthesis:

#15x^2 - 10x + 28- 10x > 4x + 10 - 5#

Combine like terms:

#15x^2 -24x+23>0#

Please observe that the leading coefficient is positive, therefore, the parabola that the quadratic describes opens upward. If the quadratic has real roots, greater than zero in the two regions to the left and right of the roots. Check whether the quadratic has real roots by evaluating the discriminant:

#b^2-4(a)(c) = (-24)^2-4(15)(23)#

#b^2-4(a)(c) = -804#

The quadratic does not have real roots, therefore, the inequality is true for all real values of x:

#{AAx |x in RR}#

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