Questions: Solve, graph, and give interval notation for the inequality: -3x-3 > -3 Interval notation for the above graph is:

Transcript text: Solve, graph, and give interval notation for the inequality: \[ -3|x-3|>-3 \] Interval notation for the above graph is: $\square$ Check Answer

Solution

Solution Steps

Step 1: Divide both sides by -3 and flip the inequality sign.

When we divide both sides of the inequality $-3|x-3| > -3$ by $-3$, we get $|x-3| < 1$. Remember that when multiplying or dividing an inequality by a negative number, the inequality sign flips.

Step 2: Rewrite the inequality as a compound inequality

$|x-3| < 1$ can be rewritten as $-1 < x-3 < 1$.

Step 3: Solve for x

Add 3 to all parts of the inequality: $-1+3 < x-3+3 < 1+3$, which simplifies to $2 < x < 4$.