Question

solve the inequality. graph the solution set and write it in interval notation. 5(x + 4)-1 > -4(x - 1)+6
choose the correct graph below.
oa. ← -1 0 → ob. ← 1 0 →
oc. ← -1 0 → od. ← -1 0 →

Explanation:

Step1: Expand both sides

Expand $5(x + 4)-1$ and $-4(x - 1)+6$.
$5(x + 4)-1=5x+20 - 1=5x + 19$, and $-4(x - 1)+6=-4x+4 + 6=-4x+10$.
So the inequality becomes $5x + 19>-4x + 10$.

Step2: Add $4x$ to both sides

To get all $x$ - terms on one side.
$5x+4x + 19>-4x+4x + 10$, which simplifies to $9x+19>10$.

Step3: Subtract 19 from both sides

$9x+19 - 19>10 - 19$, resulting in $9x>-9$.

Step4: Divide both sides by 9

$\frac{9x}{9}>\frac{-9}{9}$, so $x>-1$.

The solution set in interval - notation is $(-1,\infty)$.

The graph of the solution set has an open - circle at $x = - 1$ and a ray extending to the right.

Answer:

The correct graph is C. The solution set in interval notation is $(-1,\infty)$.