Inequality Intuition Math Example 3

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

Example 3

easy
Solve \(2x - 4 > 6\).

Solution

  1. 1
    Add 4: \(2x > 10\).
  2. 2
    Divide by 2: \(x > 5\).
  3. 3
    Solution: \(x > 5\).

Answer

\(x > 5\)
Solve like an equation: add 4, then divide by 2. Since we divided by a positive number, the direction stays the same.

About Inequality Intuition

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

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More Inequality Intuition Examples

Example 1 easy

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

Example 2 medium

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

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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