Write a compound inequality that each graph could represent
1<x<2
Sure! A compound inequality is a combination of two or more inequalities connected by the words "and" or "or". Here are a few examples of compound inequalities and the graphs they could represent:
1. Compound inequality: -3 < x ≤ 5
Graph: This compound inequality represents a shaded region on a number line that starts at -3 and goes up to, but does not include, 5. It excludes -3 but includes 5.
2. Compound inequality: x > -2 or x ≤ 6
Graph: This compound inequality represents two separate shaded regions on a number line. One region starts at -2 and extends indefinitely to the right, while the other region starts at negative infinity and goes up to, but does not include, 6. The "or" in the inequality allows for either condition to be true.
3. Compound inequality: 2x + 3 > 9 and x ≤ 4
Graph: This compound inequality represents two separate shaded regions on a coordinate plane. The first inequality, 2x + 3 > 9, represents a region above a line with a slope of 2/1 that passes through the point (3,9). The second inequality, x ≤ 4, represents a shaded region to the left of a vertical line passing through x = 4. The "and" in the inequality requires both conditions to be true.
Remember, it is important to properly interpret the inequality symbols (>, <, ≥, ≤) and the "and" or "or" connectors while graphing compound inequalities.