Question

solve the inequality. express your answer using set - notation and interval notation. graph the solution set.
-3(x + 2)<9
the solution is expressed in set notation as {x|}
the solution is expressed in interval notation as
choose the correct graph of the solution set below.
a. graph with arrows on a number - line from - 10 to 10
b. graph with arrows on a number - line from - 10 to 10
c. graph with arrows on a number - line from - 10 to 10
d. graph with arrows on a number - line from - 10 to 10
time remaining: 04:01:45

Explanation:

Step1: Expand the left - hand side

$-3(x + 2)=-3x-6$, so the inequality becomes $-3x - 6<9$.

Step2: Add 6 to both sides

$-3x-6 + 6<9 + 6$, which simplifies to $-3x<15$.

Step3: Divide both sides by - 3 and reverse the inequality sign

When dividing an inequality by a negative number, the inequality sign flips. So $\frac{-3x}{-3}>\frac{15}{-3}$, giving $x>- 5$.

Answer:

Set notation: $\{x|x > - 5\}$
Interval notation: $(-5,\infty)$
Correct graph: D (since it shows an open - circle at $-5$ and an arrow pointing to the right)