Prove that |a| < b if and only if -b < a < b

Since,

Here, the given equation is,

|a| < b

Case 1 : if a ≥ 0,

|a| < b ⇒ a < b

Case 2 : If a < 0,

|a| < b ⇒ -a < b ⇒ a > - b

( Since, when we multiply both sides of inequality by negative number then the sign of inequality is reversed. )

|a| < b ⇒ a < b or a > - b ⇒ -b < a < b

Conversely,

If -b < a < b

⇒ a < b or a > - b

⇒ a < b or -a <  b

⇒ |a| < b

Hence, proved..

answer: what are the following choices

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)