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Solve for x and graph the solution on the number line below, the graph goes from -12 to 12. -3→x/3

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To solve the inequality \(-3 \to \frac{x}{3}\), we will interpret the \(\to\) symbol as representing the "less than" symbol (i.e., \(-3 < \frac{x}{3}\)).

Let’s solve this inequality step-by-step:

  1. Start with the inequality: \[ -3 < \frac{x}{3} \]

  2. To eliminate the fraction, multiply both sides by \(3\) (note that multiplying by a positive number does not change the direction of the inequality): \[ -3 \cdot 3 < x \] \[ -9 < x \]

  3. We can also rewrite this inequality as: \[ x > -9 \]

Now, we will graph the solution \(x > -9\) on a number line from -12 to 12.

Number Line Graph

  1. The value \(-9\) will be represented on the number line.
  2. Since this is a strict inequality (>), we will use an open circle at \(-9\) (indicating that \(-9\) is not included in the solution).
  3. Shade or draw an arrow to the right from \(-9\) to indicate all numbers greater than \(-9\).

Here’s a textual representation of how the graph should look:

-12  -11  -10  -9   -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12
    |    |    |   (o)----------------------------->

In this representation:

  • The open circle at \(-9\) indicates that \(-9\) is not included in the solution.
  • The arrow points to the right, indicating that all numbers greater than \(-9\) are part of the solution set.
So x = -9?

No, \(x = -9\) is not the solution; rather, we found that \(x > -9\). This means that \(x\) can be any number greater than \(-9\).

The solution set is all real numbers greater than \(-9\). In interval notation, this is expressed as \((-9, \infty)\).

So, to clarify:

  • The solution is not just \(x = -9\).
  • The solution is \(x > -9\), which means any value larger than \(-9\) is acceptable.
Oh ok

No problem! If you have any more questions or if there's anything else you'd like to know about solving inequalities or any other topic, feel free to ask!