INEQUALITIES 3

Solve the inequality x² - 2x < 35.

solution

x² - 2x < 35

x² - 2x - 35< 0    we split -5x to get ( -7x + 5x)

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

x² - 5x - 35 < 0   

x² - 7x + 5x - 35 < 0   

(x² -7x) + (5x - 35) < 0

x(x -7) + 5(x - 7) < 0

 (x -7)(x +5) < 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 + 5 = 0; x = -5

x = 7  FALSE x = -5  TRUE

(x -7)> 0  and (x +5) < 0

so; -5 < x < 7  answer

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

Solve the inequality x² - 3x < 18.