Equations & Inequalities Mastery Worksheet
Unit 3 Review Algebra 1 Foundations
Equations & Inequalities Review
Name:
Date:
Period:
Instructions: Show all algebraic steps clearly in the boxes provided. Simplify all fractional answers.
Total: 20 Questions
1 Solving One-Step Equations (Questions 1–2)
Use inverse operations to isolate the variable
\( x - 17 = -32 \)
1 pt
Solution:
\( \frac{y}{-6} = 14 \)
1 pt
Solution:
2 Solving Two-Step Equations (Questions 3–4)
Undo addition/subtraction, then multiplication/division
\( 5m + 9 = -26 \)
2 pts
Solution:
\( \frac{w}{4} - 7 = 5 \)
2 pts
Solution:
3 Solving Multi-Step Equations (Questions 5–7)
Use Distributive Property (DP) & Combine Like Terms (CLT)
- CLT Only
\( 8p - 3 - 5p + 7 = 28 \)
\( p = \)
- Distribute
\( 4(3k - 5) = 52 \)
\( k = \)
- DP + CLT
\( 3(2x + 4) + 5x = 45 \)
\( x = \)
Unit 3: Equations & Inequalities Study Guide Page 1 of 3
Part 2 Multi-Step Practice & Solution Classification
Name:
3 Solving Multi-Step Equations Continued (Questions 8–10)
Watch negative signs during distribution!
- Neg. Distribute
\( -2(5n - 4) = 48 \)
\( n = \)
- Subtr. Parenthesis
\( 19 = 7w - (3w - 7) \)
\( w = \)
- Full Multi-Step
\( 5(2y - 1) - 4y = 31 \)
\( y = \)
4 Identifying Types of Solutions (Questions 11–16)
Solve completely, then classify the solution type
\( 6x - 7 = 2x + 17 \)
One: \( x = \) ___
No Solution
Infinite
\( 4(2a + 3) = 8a + 12 \)
One: \( a = \) ___
No Solution
Infinite
\( 5(m - 2) = 5m + 14 \)
One: \( m = \) ___
No Solution
Infinite
\( 9p - 4 = 3(3p - 1) - 1 \)
One: \( p = \) ___
No Solution
Infinite
\( 2(4k - 1) = 3(2k + 5) \)
One: \( k = \) ___
No Solution
Infinite
\( 7y + 5 - 2y = 5(y + 2) \)
One: \( y = \) ___
No Solution
Infinite
Unit 3: Equations & Inequalities Study Guide Page 2 of 3
Part 3 Inequalities & Number Line Representations
Name:
5 Graphing Inequalities (Questions 17–20)
Remember: Dividing or multiplying by a negative reverses the symbol!
17. Which graph represents the solution to the inequality: \( x - 3 \ge 1 \)? 1 pt
A. 2 3 4 5 6
B. 2 3 4 5 6
C. 2 3 4 5 6
D. 2 3 4 5 6
18. Solve and choose the correct graph for: \( -4x > 12 \) 1 pt
A. -5 -4 -3 -2 -1
B. -5 -4 -3 -2 -1
C. -5 -4 -3 -2 -1
D. -5 -4 -3 -2 -1
19. Solve and choose the correct graph for: \( 2x + 5 \le 11 \) 1 pt
A. 1 2 3 4 5
B. 1 2 3 4 5
C. 1 2 3 4 5
D. 1 2 3 4 5
20. Solve and choose the correct graph for: \( \frac{x}{-3} - 1 < 1 \) 1 pt
A. -8 -7 -6 -5 -4
B. -8 -7 -6 -5 -4
C. -8 -7 -6 -5 -4
D. -8 -7 -6 -5 -4
Self-Check & Test Readiness
Did you isolate terms using inverse operations?
Did you reverse the inequality when multiplying/dividing by a negative?
Did you check: false statement = No Solution; identity = Infinite Solutions?
Confidence: 1 (Need Help) — 5 (Mastered): [ ] / 5
Unit 3: Equations & Inequalities Study Guide Page 3 of 3
