Question

solve the inequality. graph the solution set and write it in interval
3(x + 4)-1> - 5(x - 5)+10

choose the correct graph below.

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Explanation:

Step1: Expand both sides

$3(x + 4)-1=3x+12 - 1=3x + 11$ and $-5(x - 5)+10=-5x+25 + 10=-5x+35$. So the inequality becomes $3x + 11>-5x+35$.

Step2: Add $5x$ to both sides

$3x+5x + 11>-5x+5x+35$, which simplifies to $8x + 11>35$.

Step3: Subtract 11 from both sides

$8x+11 - 11>35 - 11$, resulting in $8x>24$.

Step4: Divide both sides by 8

$\frac{8x}{8}>\frac{24}{8}$, so $x > 3$.
The solution set in interval - notation is $(3,\infty)$. On a number - line, it is an open circle at 3 and a ray pointing to the right.

Answer:

The graph with an open circle at 3 and a ray pointing to the right (assuming one of the options has this characteristic). Since the options are not fully visible, but based on the solution $x>3$, the correct graph should have an open - circle at 3 and an arrow extending to the right on the number line.