Use the number line to represent the solution to 120x + 180 ≤ 1020

Question

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Answer 1

To solve the inequality \(120x + 180 \leq 1020\), we first isolate \(x\).

1. Subtract \(180\) from both sides: \[ 120x \leq 1020 - 180 \] \[ 120x \leq 840 \]

2. Next, divide both sides by \(120\): \[ x \leq \frac{840}{120} \] \[ x \leq 7 \]

Now that we have the solution \(x \leq 7\), we can represent this on a number line.

Number Line Representation:

1. Draw a horizontal line to represent the number line.
2. Mark a point at \(7\) on the line.
3. Since the solution includes \(7\) (due to "less than or equal to"), we use a closed circle at \(7\).
4. Shade the line to the left of \(7\) to indicate all numbers less than \(7\) are included in the solution.

The representation would look like this:

<---|---|---|---|---|---|---|---|---|--->
    0   1   2   3   4   5   6   7   8   9
                     ●
                     <-----------

In this illustration, the point \(7\) is closed (indicating it is included in the solution), and the shading extends to the left to indicate all values less than \(7\) are part of the solution set.