Solve the inequality. Graph the solution set and write it in interval notation.
4/9x>2
To solve the inequality 4/9x > 2, we need to multiply both sides of the inequality by 9 to get rid of the fraction. However, since we are multiplying by a negative number, we need to change the direction of the inequality sign.
Multiplying both sides of the inequality by 9, we get:
(4/9)(9x) > 2(9)
4x > 18
Now, we can divide both sides of the inequality by 4:
(4x)/4 > 18/4
x > 4.5
Therefore, the solution set for the inequality 4/9x > 2 is x > 4.5.
Graphically, this inequality represents all values of x that are greater than 4.5 on the number line. We can represent this graphically by shading the region to the right of 4.5 on the number line.
In interval notation, the solution set is (4.5, ∞).