2-how-to-solve-linear-inequalities-mathbff

MIT grad shows how to solve an inequality. This video focuses on linear inequalities. More videos with Nancy coming in 2017!

A linear inequality is a linear equation that uses an inequality symbol instead of an equality symbol (=). One example is 2x + 3 ≤ 11. Solving for x is the same as solving a linear equality (-2x + 3 = 11) EXCEPT that if you ever have to DIVIDE by a NEGATIVE number or MULTIPLY by a NEGATIVE number while solving for x, you must switch the direction of your inequality symbol (≤ becomes ≥, for example).

For example, for the linear inequality -2x + 3 ≤ 11, to try to get x alone, first move the constant 3 to the right side by subtracting 3 from both sides. This gives -2x ≤ 8. Next, to get x alone, divide out -2 from both sides, but because you're dividing by a negative number you must flip the direction of the inequality symbol from ≤ to ≥ so this gives x ≥ -4.

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