Benchmarks

32

ELEMENTARY ALGEBRA

12. $a\; +\; [b\; -\; (a\; -\; b)]$ .

13. $a\; +\; b\; -\; [(b\; +\; d)\; -\; (a\; -\; b)]$ .

14. $m\; -\; (n\; -\; p)\; +\; [3m\; -\; \backslash overline\{3n\; -\; 6m\}]$ .

15. $a\; -\; [a\; -\; \backslash \{a\; -\; (-a)\backslash \}]$ .

16. $x\; -\; [3y\; +\; \backslash \{3z\; -\; (z\; -\; x)\; +\; y\backslash \}\; -\; 2x]$ .

17. $-[m\; -\; (m\; +\; n)\; -\; (m\; -\; n)\; -\; (-m\; +\; n)]$ .

18. $12a\; -\; \backslash \{(a\; +\; b)\; -\; [b\; -\; (\backslash overline\{a\; -\; b\})]\; -\; a\backslash \}$ .

19. $2x\; -\; \backslash \{x\; -\; (x\; -\; y)\; -\; [\backslash overline\{x\; -\; x\; -\; y\}]\; -\; y\backslash \}$ .

20. $12\; -\; 2a\; -\; \backslash \{-a\; -\; [2a\; -\; (a\; -\; \backslash overline\{7\; -\; a\})]\backslash \}.$

21. $14\; -\; 3a\; -\; \backslash \{9a\; -\; [10a\; -\; (11a\; -\; \backslash overline\{6\; -\; 6a\})]\backslash \}.$

22. $a\; -\; [-\backslash \{-(-a)\backslash \}]$ .

23. $a\; -\; 3\; -\; [-\backslash \{-(\backslash overline\{-a\; +\; a\; +\; b\})\backslash \}]$ .

24. $x\; +\; y\; -\; [-(x\; -\; y)\; +\; \backslash \{-x\; +\; (\backslash overline\{x\; -\; x\; -\; y\})\backslash \}]$ .

25. $1\; -\; \backslash \{-a\; -\; (a\; +\; 1)\; -\; [-a\; -\; (\backslash overline\{a\; -\; a\; -\; 1\})]\backslash \}.$

26. $a\; -\; (-\backslash left\backslash \{-\backslash left[-(-a)\backslash right]\backslash right\backslash \})$ .

27. $1\; -\; (-\backslash \{a\; +\; (-a\; +\; 1)\backslash \})\; -\; \backslash \{\backslash overline\{a\; -\; a\; -\; 1\}\backslash \}.$

28. $6m\; +\; \backslash \{4m\; -\; [8n\; -\; (2m\; +\; 4n)\; -\; 22n]\; -\; 7n\backslash \}$
$+\; [9m\; -\; (3n\; +\; 4m)\; +\; 14n]$ .

29. $1247\; -\; [1722\; -\; \backslash \{1722\; +\; (933\; -\; 1247)\backslash \}]$ .

30. From $a\; +\; \backslash \{(4\; -\; b)\; +\; (a\; -\; 4)\; -\; \backslash overline\{a\; -\; 7\}\backslash \}$ subtract
$a\; -\; \backslash \{(6\; -\; b)\; +\; (6a\; -\; 6)\; -\; (5a\; -\; 7)\backslash \}$ .

31. From the sum of $a\; +\; \backslash \{a\; -\; (b\; -\; c)\backslash \}$ and
$-a\; +\; [4a\; -\; (5b\; +\; c)]$ subtract $a\; -\; (b\; -\; c)$ .

32. Simplify $4a\; -\; [6b\; +\; (3a\; -\; c)\; -\; \backslash \{\backslash overline\{5b\; -\; c\; -\; a\}\backslash \}]$ and check
the answer by substituting $a=3$ , $b=2$ , $c=1$ in the question
and the answer.

33. Simplify $9a\; -\; [-7a\; +\; \backslash \{5b\; -\; (a\; -\; b)\; +\; \backslash overline\{a\; -\; b\}\backslash \}]$ and
check the answer by the substitution $a\; =\; 1$ , $b\; =\; 2$ .