Solve the inequality and graph the solution.

Question

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3+2w≤1

Answer 1

To solve the inequality \(-3 + 2w \leq 1\), we will isolate \(w\).

1. Start by adding \(3\) to both sides of the inequality: \[ -3 + 2w + 3 \leq 1 + 3 \] Simplifying this gives: \[ 2w \leq 4 \]

2. Now, divide both sides by \(2\): \[ \frac{2w}{2} \leq \frac{4}{2} \] This simplifies to: \[ w \leq 2 \]

The solution to the inequality is: \[ w \leq 2 \]

Graphing the Solution

To graph \(w \leq 2\):

1. Draw a number line.
2. Place a closed dot on the number \(2\) to indicate that \(2\) is included in the solution.
3. Shade the line to the left of \(2\) to represent all numbers less than or equal to \(2\).

Here's a representation of the graph:

<---|----|----|----|----|----|----|----|----|----|---->
    -2   -1    0    1    2    3    4
          ●<==================

This indicates that all values of \(w\) to the left of \(2\) (including \(2\) itself) are part of the solution.