Solving Linear Inequalities Flashcards

All 6 cards in this deck

How do you solve a one-step linear inequality?

e.g. $x + 7 > 10$

Do the same inverse operation to both sides, keeping the inequality sign.

e.g. subtract 7: $x > 3$.

What are the steps to solve a two-step linear inequality?

e.g. $7x - 27 < 8$

1. Add or subtract to isolate the term in $x$: $7x < 35$.
2. Divide both sides by the coefficient: $x < 5$.
3. Write the answer as an inequality, not an equation: $x < 5$.

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

e.g. $3x + 5 \ge x + 17$

1. Collect the $x$ terms on one side: $2x + 5 \ge 17$.
2. Collect the numbers on the other side: $2x \ge 12$.
3. Divide by the coefficient of $x$: $x \ge 6$.

What is the first step in solving a linear inequality containing brackets?

e.g. $2(x + 3) \le 10$

Expand the brackets.

e.g. $2x + 6 \le 10$, giving $x \le 2$.

True or false? An answer of $x = 6$ is an acceptable solution to the inequality $3x + 5 \ge x + 17$.

False. The solution set must be written as an inequality: $x \ge 6$.

After solving an inequality, how do you find the greatest integer that satisfies it?

e.g. $5y - 7 < 16$ gives $y < 4.6$

Take the largest whole number below the critical value (or equal to it if the sign is $\le$).

e.g. $4$.