Solving Linear Inequalities Flashcards

All 6 cards in this deck

What are the steps to solve a linear inequality with the unknown on both sides?

e.g. $14n > 11n + 6$

1. Collect the unknown on one side: $3n > 6$
2. Divide both sides by the coefficient: $n > 2$

What must you do to the inequality sign when you multiply or divide both sides by a negative number?

Reverse it.
e.g. $-2x < 6$ gives $x > -3$

What are the steps to solve a double-sided inequality?

e.g. $-2 < x + 3 \le 4$

1. Do the same operation to all three parts: $-2 - 3 < x \le 4 - 3$
2. Simplify: $-5 < x \le 1$

When showing an inequality on a number line, when do you use an open circle and when a closed (filled) circle?

Open circle for $<$ or $>$ (value not included); closed circle for $\le$ or $\ge$ (value included).

How do you write a solution in set notation?

e.g. the solution $-5 < x \le 1$

$\{x : -5 < x \le 1\}$

True or false? If $n$ is an integer and $-2 \le n < 5$, the greatest possible value of $n$ is $5$.

False. It is $4$, because $5$ is not included by the strict $<$ sign.