solve compound inequality. state solution set using interval notation and graph it.

Question

1/3x>2 and 1/4x>2.

Answer 1

The compound inequality is 1/3x > 2 and 1/4x >2.

The first inequality is 1/3x > 2.

Multiply 3x to each side.

1 > 6x

Divide each side by 6.

1/6 > x

x < 1/6 = 1.67.

 

The second inequality is 1/4x > 2.

Multiply 4x to each side.

1 > 8x

Divide each side by 8.

x < 1/8 = 0.125.

The solution of the compound inequality is x < 1/6 and x < 1/8.

The above solution can be written as {x | x < 1/8}.

The interval notation form of solution is (- ∞, 1/8).

 

The solution set graph is

Observe the graph, the open circle means that 1/8 is not a solution of the compound inequality.