Solve 7(x+4)-⅔(x-6)≤2(x-3)(x+5)]

Answer 1

This doesn't seem to work out nicely:

Distribute and multiply out:

7x + 28 -(2/3)x + 4 ≤ 2x² + 4x - 30

Put everything on one side for quadratic

0 ≤ 2x² -(7/3)x - 62

multiply through by 3 to make the coefficients easier to deal with

0 ≤ 6x² -7/x - 186

Solve quadratic for the equality to find critical x's (This will demarcate ranges that are above and below zero.

Using quadratic formula: x = (1/12) (7 ± sqrt( 7²-4(6)(-186))) = (-5.015 and 6.182)

The inequality holds for x ≤ -5.015 and ≥6.182 (check point like x = 0 quadratic is <0, so this area is excluded.

Please consider a tutor. Take care