Show that 5x²+2x-3 can be written in the
form |x+1/5| < 4/5 Hence, solve
the inequality
5x²+2x-3< 0

5x² + 2x - 3 < 0

5x² + 2x < 3

x² + 2/5 x < 3/5

Complete the square on the left side:

x² + 2/5 x + 1/25 - 1/25 < 3/5

(x + 1/5)² - 1/25 < 3/5

(x + 1/5)² < 16/25

Take the square root of both sides, keeping in mind that √(x²) = |x| for all x.

√((x + 1/5)²) < √(16/25)

|x + 1/5| < 4/5

This means

-4/5 < x + 1/5 < 4/5

-1 < x < 3/5

step-by-step explanation:

bob the banana