graph of the compound inequality

Question

x-2>-3x <12

Answer 1

The compound inequalities  are   x -2 > -3x and -3x < 12

= x -2 > -3x

= -2 > -4x

Multiply each side by negative one and flip the symbol

= 4x < 2

Therefore x < 1/2

= -3x < 12

= 3x > -12

Therefore x > -4

The inequality solution is -4 < x < 1/2

Graph of the compound inequality is 

Comments

Solution set {x |  x > 1/2 }.

Graph of the compound inequality is

Answer 2

The inequality is x -2 > -3x < 12

The compound inequalities are  x - 2 > -3x and -3x < 12

Case1: Solve the inequaliy x - 2 > - 3x

x + 3x -2 > 0

4x > 2

x > 2/4

x > 1/2

The solution is x > 1/2

Case2: Solve the inequality -3x < 12

-x < 12/3

-x < 4

Multiply each side by negative one and flip the symbol.

x > -4

Soluition is x > -4

Compound inequality solution is intersection of two inequalities .

The compound inequality solution is {x|x: x > 1/2}

Graph of the compound inequality is