Equations and Inequalities — Algebra 2 Unit 1 practice.
This unit covers absolute value equations, compound inequalities and literal equations — essential concepts for Algebra 2. Use our interactive study games to test your understanding, or review questions in traditional format below.
Pick a mode. Play.
Answer questions as fast as you can. 2 minutes on the clock. Build streaks for bonus points!
Don't want to play?
Review the questions traditionally. Click to expand.
Questions loading...
Focus on understanding.
Focus on understanding core concepts before memorizing details. Use the game modes to test yourself repeatedly — spaced repetition is proven to boost long-term retention.
Related units
This unit covers absolute value equations, compound inequalities and literal equations — essential concepts for Algebra 2. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Absolute Value Equations
Absolute value equations require splitting into two cases: one where the expression inside equals the positive value, and one where it equals the negative value. Students must check for extraneous solutions by substituting answers back into the original equation. If the absolute value equals a negative number, the equation has no solution.
Key Points
- |ax + b| = c splits into ax + b = c AND ax + b = -c (when c ≥ 0)
- Always check solutions — extraneous answers can appear
- If c < 0, write 'no solution' immediately
- Isolate the absolute value expression before splitting into two cases
Solve: |2x - 3| = 7
Split into two equations: 2x - 3 = 7 and 2x - 3 = -7. Solving the first gives x = 5; solving the second gives x = -2. Both check out in the original equation, so the solution set is {-2, 5}.
2 Compound Inequalities
Compound inequalities join two inequalities with 'and' (intersection) or 'or' (union). An 'and' inequality requires both conditions to be true simultaneously, producing a bounded interval; an 'or' inequality requires at least one condition to be true, often producing two separate rays. Students must graph the solution on a number line and write it in interval notation or set-builder notation.
Key Points
- 'And' compound inequalities: solve both, take the overlap (intersection)
- 'Or' compound inequalities: solve both, take all values from either (union)
- Flip the inequality sign when multiplying or dividing by a negative number
- A three-part inequality like -2 < 3x + 1 ≤ 10 is solved by operating on all three parts simultaneously
Solve and graph: -2 < 3x + 1 ≤ 10
Subtract 1 from all three parts: -3 < 3x ≤ 9. Divide all parts by 3: -1 < x ≤ 3. The solution is the interval (-1, 3], graphed as an open circle at -1 and a closed circle at 3 with shading in between.
3 Literal Equations
A literal equation contains multiple variables, and the goal is to isolate one specific variable using inverse operations — the same process as solving a regular equation, but with letters instead of numbers. Students must treat all other variables as constants while isolating the target variable. These appear on exams both as standalone problems and embedded in formula-based word problems.
Key Points
- Use inverse operations to isolate the target variable — same steps as numeric equations
- Treat all non-target variables as if they were numbers (constants)
- Factoring is required when the target variable appears in more than one term (e.g., ax + bx = c → x(a + b) = c)
- Common formulas tested: A = ½bh, PV = nRT, y = mx + b
Solve for x: ax + bx = c
Factor x out of the left side: x(a + b) = c. Divide both sides by (a + b): x = c / (a + b). This works as long as a + b ≠ 0; recognizing when to factor is the key skill tested here.
Questions, answered.
What is Equations and Inequalities?
Equations and Inequalities is Unit 1 of Algebra 2, covering absolute value equations, compound inequalities and literal equations.
How to study for Algebra 2 Unit 1?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 27+ review questions across 5 different game modes.