Question

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

Explanation:

Step1: Move terms with x to one - side

Subtract $\frac{x}{3}$ from both sides and add 10 to both sides: $\frac{4}{9}x-\frac{x}{3}>-12 + 10$.

Step2: Find a common denominator for x - terms

The common denominator of 9 and 3 is 9. So $\frac{4}{9}x-\frac{3}{9}x>-2$, which simplifies to $\frac{4x - 3x}{9}>-2$.

Step3: Simplify the left - hand side

We get $\frac{x}{9}>-2$.

Step4: Solve for x

Multiply both sides by 9: $x>-18$.

Answer:

The solution is all values of x greater than - 18. On the number - line, you would drag the open - circle (since the inequality is >, not $\geq$) to the point at - 18 and shade to the right.