Notes
Inequalities and their graphs
Inequalities use $<$, $>$, $\le$ and $\ge$. On a number line, an open circle means the endpoint is not included and a closed circle means it is. "At least" is $\ge$ and "at most" is $\le$.
Solving
Solve like an equation, but flip the sign when you multiply or divide by a negative. Check with a number from your answer.
Compound and absolute value inequalities
- And: both parts true (the overlap). Or: either part true.
- $|x - c| < a$ becomes $c - a < x < c + a$.
- $|x - c| > a$ becomes $x < c - a$ or $x > c + a$.
Topics in this unit
Each topic has its own short notes and practice.
Practice
$-3x \ge 15$, then divide by $-3$ and flip.
The total cost can't be more than $40.
Add 6: $2 < 2x \le 14$. Divide by 2.
$2x - 3 < -5$ or $2x - 3 > 5$.
An absolute value can never be less than a negative number.
Closed circles include both endpoints.
Free response
Write your answer first, then open the scoring guide.
Free-response question
A student earns $12 per hour at a part-time job and wants to earn at least $300 this month, but can work at most 30 hours.
(a) Write an inequality for the number of hours $h$ needed to earn at least $300, and solve it.
Show the answer and scoring guide
$12h \ge 300$, so $h \ge 25$.
Check off the points you earned:
(b) Write a compound inequality for all possible numbers of hours that meet both goals.
Show the answer and scoring guide
$25 \le h \le 30$
Check off the points you earned:
(c) Can the student reach the goal working 24 hours if they get a $10 bonus? Explain.
Show the answer and scoring guide
$12(24) + 10 = 298$, which is less than $300, so no.
Check off the points you earned: