Question

solve 2r - 8 > $\frac{3}{4}(r - 6)$. solution: graph the solution.

Explanation:

Step1: Expand the right - hand side

$2r - 8>\frac{3}{4}r-\frac{3}{4}\times6$, so $2r - 8>\frac{3}{4}r-\frac{9}{2}$.

Step2: Move the terms with $r$ to one side

$2r-\frac{3}{4}r>8 - \frac{9}{2}$.

Step3: Combine like terms

$\frac{8r - 3r}{4}>\frac{16 - 9}{2}$, so $\frac{5r}{4}>\frac{7}{2}$.

Step4: Solve for $r$

Multiply both sides by $\frac{4}{5}$, we get $r>\frac{7}{2}\times\frac{4}{5}$, so $r>\frac{14}{5}$.

Answer:

$r>\frac{14}{5}$; The graph should have an open - circle at $\frac{14}{5}$ (or $2.8$) and an arrow pointing to the right.