Question

6< 5x -9 < 11Graph the solution set on a number line

Answer 1

we have the compound inequality

6< 5x -9 < 11

step 1

solve

5x -9 < 11

5x < 11+9

5x < 20

x < 4

solution 1 is the interval (-infinite, 4)

step 2

solve

6< 5x -9

6+9 < 5x

15 < 5x

3 < x

rewrite

x >3

solution 2 is the interval (3, infinite)

step 3

the solution of the compound inequality is

(-infinite, 4) ∩ (3, infinite)=(3,4)

the solution in a number line is the shaded area between the numbers 3 (open circle and 4 (open circle)

see the attached figure