If `-3x+17 lt -13`, then

Options

A. `x in (10, infty)`
B. `x in [10, infty)`
C. `x in (-infty, 10]`
D. `x in [-10, 10)`

Explanation

To solve the inequality \(-3x + 17 < -13\), we can follow these steps:

### Step 1: Isolate the term with \(x\)
We start with the inequality:
\[ -3x + 17 < -13 \]
Subtract \(17\) from both sides:
\[ -3x < -13 - 17 \]

### Step 2: Simplify the right side
Now, simplify the right side:
\[ -3x < -30 \]

### Step 3: Divide by \(-3\)
Next, we divide both sides by \(-3\). Remember that when we divide or multiply both sides of an inequality by a negative number, we must flip the inequality sign:
\[ x > 10 \]

### Step 4: Write the solution in interval notation
The solution \(x > 10\) can be expressed in interval notation as:
\[ (10, \infty) \]

### Final Answer
Thus, the solution to the inequality \(-3x + 17 < -13\) is:
\[ x > 10 \quad \text{or} \quad x \in (10, \infty) \]

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