INEQUALITIES 10

Solve the inequality x² - 5x < 14.

solution

x² - 5x < 14

x² - 5x - 14 < 0    we split -5x to get ( -7x + 2x)

(-7x + 2x) = -5x    and  (-7x x 2x) = -14x²

x² - 5x - 14 < 0   

(x² -7x) + (2x - 14) < 0

x(x -7) + 2(x - 7) < 0

 (x -7)(x +2) < 0 ------- (i)

Equation (i) above will be true for any value less than zero, that is all negative numbers are less than zero.

When x - 7 = 0;  x =7

When x + 2 = 0; x = -2

x = 7  FALSE x = -2  TRUE

(x -7)> 0  and (x +2) < 0

so; -2 < x < 7  answer

TRY THIS.....................

Solve the inequality x² - 5x < 36.