- $ax = b$
- $x/a = b, a ≠ 0$
- $ax + b = c$
- $x/a + b = c, a ≠ 0$
- $a(x + b) = c$
[C, CN, PS, V]
(a) |
Identify and describe situations, which are relevant to self, family, or community, that can be modeled by a linear equation (e.g., the cost of purchasing x fish from a fisherman). |
(b) |
Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and describe the process orally and symbolically. |
(c) |
Discuss the importance of the preservation of equality when solving equations. |
(d) |
Explain the meaning of and verify the solution of a given linear equation using a variety of methods, including concrete materials, diagrams, and substitution. |
(e) |
Generalize and apply symbolic strategies for solving linear equations. |
(f) |
Identify, explain, and correct errors in a given solution of a linear equation. |
(g) |
Demonstrate the application of the distributive property in the solving of linear equations. E.g. $2(x + 3); 2x + 6 = 5$ |
(h) |
Explain why some linear relations. E.g. $x/a = b, a ≠ 0$ and $x/a + b = c, a ≠ 0$ have a given restriction and provide an example of a situation in which such a restriction would be necessary. |
(i) |
Identify and solve problems that can be represented using linear equations and explain the meaning of the solution in the context of the problem. |
(j) |
Explain the algebra behind a particular algebra puzzle such as this puzzle written for 2008:
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