Answers:
- Compound inequality: 1 < x < 6
- Graph: Open hole at 1 and 6, shading in between (see diagram below)
- Interval notation: (1,6)
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Work Shown:
3 < 2x+1 < 13
3-1 < 2x+1-1 < 13-1 .... subtract 1 from all sides
2 < 2x < 12
2/2 < 2x/2 < 12/2 ... divide both sides by 2
1 < x < 6
The value of x is between 1 and 6, excluding both endpoints.
Since we exclude both endpoints, the graph will have open holes at 1 and 6 on the number line. The shading is between the open holes. The graph is below.
Converting 1 < x <6 to interval notation leads to (1, 6)
The curved parenthesis in interval notation indicate "exclude the endpoint".
