Which number line represents the solution of [tex]x+3\ \textgreater \ 2[/tex]?
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Answer (2)
Solve the inequality 2"> x + 3 > 2 by subtracting 3 from both sides.
Simplify to get -1"> x > − 1 .
Represent the solution on a number line with an open circle at -1 and shading to the right.
The solution is -1}"> x > − 1 .
Explanation
Understanding the Problem We are given the inequality 2"> x + 3 > 2 and need to find the number line that represents its solution.
Isolating x To solve the inequality, we need to isolate x on one side. We can do this by subtracting 3 from both sides of the inequality: 2-3"> x + 3 − 3 > 2 − 3
Simplifying the Inequality Simplifying the inequality, we get: -1"> x > − 1
Interpreting the Solution This means that the solution to the inequality is all numbers greater than -1. On a number line, this is represented by an open circle at -1 (since -1 is not included in the solution) and shading to the right (representing all numbers greater than -1).
Conclusion Therefore, the correct number line should have an open circle at -1 and be shaded to the right. Without the actual number lines to compare, we can describe what the correct one should look like.
Examples
Imagine you're measuring the temperature required for a science experiment. The inequality -1"> x > − 1 means you need the temperature to be strictly above -1 degree Celsius for the experiment to work. This concept is also used in setting minimum speed limits on roads or minimum age requirements for certain activities.
The solution to the inequality 2"> x + 3 > 2 is -1"> x > − 1 . This is represented on a number line with an open circle at -1 and shading to the right. Without the number lines to select from, identify the one with the correct markings for this solution.
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