Inequality Intuition Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumSolve \(-2x \geq 8\) and explain the direction flip when multiplying by a negative.
Solution
- 1 Divide both sides by \(-2\). When dividing by a negative, flip the inequality.
- 2 \(-2x \geq 8 \Rightarrow x \leq -4\).
- 3 Solution: all \(x \leq -4\).
- 4 Check with \(x=-6\): \(-2(-6) = 12 \geq 8\) ✓; check \(x=-4\): \(-2(-4)=8 \geq 8\) ✓.
Answer
\(x \leq -4\)
Dividing or multiplying an inequality by a negative number flips the inequality direction. This preserves the truth of the statement.
About Inequality Intuition
Understanding that and describe ordering relationships—one quantity is strictly smaller or larger than the other.
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