Algebra, Abstracted

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Worksheet Algebra, Abstracted

It’s time to solve some algebra problems. But numbers are boring, so let’s use some other symbols. To help make sense of these symbols, “addition” and “multiplication” tables are provided. For example, from the second table you can conclude that \(🍄\cdot 🐧 = 🞛\text{.}\)

+	⚝	🍄	🐧	🞛	🙂	⛏
⚝	⚝	⚝	⚝	⚝	⚝	⚝
🍄	⚝	🍄	🐧	🞛	🙂	⛏
🐧	⚝	🐧	⛏	🍄	⚝	🞛
🞛	⚝	🞛	🍄	🙂	💩	🐧
🙂	⚝	🙂	⚝	💩	🐧	⛏
⛏	⚝	⛏	🞛	🐧	⛏	🞛

\(\cdot\)	⚝	🍄	🐧	🞛	🙂	⛏
⚝	⚝	🍄	🐧	🞛	🙂	⛏
🍄	🍄	⚝	🞛	🐧	⛏	🙂
🐧	🐧	⛏	🙂	🍄	⚝	🞛
🞛	🞛	🙂	⛏	⚝	🍄	🐧
🙂	🙂	🞛	⚝	⛏	🐧	🍄
⛏	⛏	🐧	🍄	🙂	🞛	⚝

Warm up.

To get started, do some arithmetic. Complete the following computations:

1.

\(🍄 + 🙂 = \)

2.

\(🙂 + 🞛 + ⛏ =\)

3.

\(⛏ + 🞛\cdot⛏ =\)

4.

\(🐧 \cdot 🞛 = \)

5.

\(2🐧 = \)

6.

\(🐧^3 = \)

Solve for \(x\text{,}\) if possible.

7.

\(🐧\cdot x = 🍄\)

8.

\(x \cdot 🐧 = 🍄\)

9.

\(x + 🐧 = 🍄\)

10.

\(x + ⛏ = ⛏\)

11.

\(x \cdot ⛏ = ⛏\)

12.

\(x^2 = 🙂\)

13.

\(🍄 \cdot x = 🙂 \cdot x\)

14.

\(🍄 \cdot x + 🙂 = 🐧\)

15.

\(⛏ \cdot x + 🞛 = 🍄\)

16.

\(🙂\cdot x^2 + 🞛 = 🐧\)

17.

\(🍄 \cdot x^2 + 🙂 \cdot x + 🞛 = 🐧\)