How do you solve 3 abs( x + 5 ) < 21 ?

2 Answers
Apr 29, 2015

x<2 or x> -12

Solution

3abs(x+5)<21

abs(x+5)<21/3

abs(x+5)<7

It has two solutions

Either

x+5<7 ......(i)

Or

x+5> -7.....(ii)

Solving (i)

x+5-5<7-5

x+cancel5-cancel5<2

x<2

Now, on solving (ii)

x+5-5> -7-5

x+cancel5-cancel5> -12

x> -12

Apr 29, 2015

We can divide both sides by 3 to get

abs(x+5) < 21/3

->abs(x+5) < 7

This tells us that x+5 will lie between -7 and 7:

-7 < x + 5 < 7

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

color(green)( -12 < x < 2

To verify your answer , choose appropriate values of x and see if the inequality is satisfied

  • Say x = -10

Left hand side = 3*abs(-10+5) = 3*abs(-5) = 3*5 = 15 (<21)

  • Say x = 1

Left hand side = 3*abs(1+5) = 3*abs(6) = 3*6 = 18 (<21)