Question

graph the solution of this inequality:
\frac{4}{9}x - 10 > \frac{x}{3} - 12

drag a point to the number line.

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the inequality \(\frac{4}{9}x - 10>\frac{x}{3}-12\) by \(9\) (the least - common multiple of \(9\) and \(3\)):
\(9\times(\frac{4}{9}x - 10)>9\times(\frac{x}{3}-12)\)
\(4x-90 > 3x - 108\)

Step2: Move the terms with \(x\) to one side and constants to the other side

Subtract \(3x\) from both sides: \(4x-3x-90>3x - 3x-108\), which gives \(x-90>-108\)
Then add \(90\) to both sides: \(x-90 + 90>-108 + 90\)
\(x>-18\)

Answer:

The solution of the inequality is \(x > - 18\). On the number - line, we use an open circle at \(-18\) (because the inequality is strict, \(x
eq - 18\)) and draw an arrow to the right.