Study Guide — HSA.REI.D.11
Explain why the x-coordinates of the points where the graphs of the e…
Solve equations and inequalities and justify each step.
What this standard means
- Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
- Apply explain why the x-coordinates of the points where the graphs of the e… with models and explanation
- Solves linear and quadratic equations
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Do the same operation to both sides 2. Graph solutions on a number line 3. Check solutions by substitution
_See printable PDF for diagram._
Common mistakes
- Dividing by zero
- Reversing inequality when multiplying by negative
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSA.REI.D.11.
- [ ] Solves linear and quadratic equations
- [ ] Solves inequalities and graphs solutions
- [ ] Justifies steps algebraically
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors