- Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
- Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

**Subject Area:**Mathematics

**Grade:**8

**Domain-Subdomain:**Expressions & Equations

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Analyze and solve linear equations and pairs of simultaneous linear equations. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

### Remarks/Examples

**Fluency Expectations or Examples of Culminating Standards**

Students have been working informally with one-variable linear equations since as early as kindergarten. This important line of development culminates in grade 8 with the solution of general one-variable linear equations, including cases with infinitely many solutions or no solutions as well as cases requiring algebraic manipulation using properties of operations. Coefficients and constants in these equations may be any rational numbers.

**Examples of Opportunities for In-Depth Focus**

This is a culminating standard for solving one-variable linear equations.

### TEST ITEM SPECIFICATIONS

### SAMPLE TEST ITEMS (6)

**Test Item #:**Sample Item 1**Question:**How many solutions does the equation shown have?**Difficulty:**N/A**Type:**OR: Open Response

**Test Item #:**Sample Item 2**Question:**What values of a and b would make the equation shown have infinitely many solutions?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 3**Question:**Solve the equation shown for x.

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 4**Question:**Explain why has no solution. Choose the best response.

**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 5**Question:**Enter values of a and b for which x = 4 is a solution of the equation shown.

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 6**Question:**Select whether each equation has no solution, one solution, or infinitely many solutions.

**Difficulty:**N/A**Type:**MI: Matching Item