Study Guide — HSA.REI.D.12

Graph the solutions to a linear inequality in two variables as a half…

Solve equations and inequalities and justify each step.

What this standard means

• Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
• Apply graph the solutions to a linear inequality in two variables as a half… 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.12.

• [ ] 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