Questions: Solve the inequality. Graph the solution set and write it in interval notation. -3<3(x-3) ≤ 9 Write the solution in interval notation. (Type your answer in interval notation.)

Solve the inequality. Graph the solution set and write it in interval notation.
-3<3(x-3) ≤ 9

Write the solution in interval notation.
(Type your answer in interval notation.)

Transcript text: Solve the inequality. Graph the solution set and write it in interval notation. \[ -3<3(x-3) \leq 9 \] Write the solution in interval notation. $\square$ (Type your answer in interval notation.)

Solution

Solution Steps

Step 1: Divide by 3

Divide all parts of the compound inequality by 3: $-3 < 3(x-3) \leq 9$ becomes $-1 < x-3 \leq 3$

Step 2: Add 3

Add 3 to all parts of the inequality: $-1 + 3 < x-3 + 3 \leq 3 + 3$ simplifies to $2 < x \leq 6$

Step 3: Interval Notation

The solution in interval notation is $(2, 6]$. This represents all numbers greater than 2 and less than or equal to 6. The parenthesis indicates 2 is not included, and the bracket indicates 6 is included. This corresponds to graph B in the prompt (a number line with an open circle at 2 and a closed circle at 6, shaded between).

Final Answer:

$(2, 6]$ Graph B

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