Question

solve the inequality. graph the solution set and write it in

$\frac{1}{5}(x + 5)<\frac{1}{6}(3x + 2)$

choose the correct graph below.

a.
<graph with arrow pointing right starting from -10 and ending at 20/9>

c.
<graph with arrow pointing left starting from -10 and ending at 20/9>

write the answer in interval notation.

(type your answer in interval notation. use integers or fraction)

Explanation:

Step1: Eliminate fractions

Multiply both sides by 30 (LCM of 5 and 6) to get $30\times\frac{1}{5}(x + 5)<30\times\frac{1}{6}(3x + 2)$. This simplifies to $6(x + 5)<5(3x + 2)$.

Step2: Expand expressions

Expand the brackets: $6x+30 < 15x+10$.

Step3: Isolate x - terms

Subtract 6x from both sides: $30<15x - 6x+10$, which gives $30 < 9x+10$.

Step4: Further isolate x - terms

Subtract 10 from both sides: $30 - 10<9x$, so $20 < 9x$.

Step5: Solve for x

Divide both sides by 9: $x>\frac{20}{9}$.

The solution set on a number - line has an open circle at $\frac{20}{9}$ and the line extends to the right.

Answer:

A. (since the correct graph has an open circle at $\frac{20}{9}$ and the line extends to the right), $(\frac{20}{9},\infty)$