Inequality Intuition Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Solve \(x + 3 < 10\) and graph the solution on a number line.

Solution

  1. 1
    Subtract 3 from both sides: \(x < 7\).
  2. 2
    Solution: all numbers less than 7.
  3. 3
    Graph: open circle at 7, arrow pointing left.
  4. 4
    Example values: \(x = 6, 5, 0, -1, \ldots\)

Answer

\(x < 7\)
Inequalities are solved like equations but with a direction. The solution is a range of values, not a single point. Open circle means 7 is not included.

About Inequality Intuition

Understanding that << and >> describe ordering relationships—one quantity is strictly smaller or larger than the other.

Learn more about Inequality Intuition →

More Inequality Intuition Examples

Example 2 medium

Solve (-2x geq 8) and explain the direction flip when multiplying by a negative.

Example 3 easy

Solve (2x - 4 > 6).

Example 4 medium

A student must score at least 70 to pass. They have scores 65, 72, 80. Which scores pass? Write as i

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