1) 2 * ( x + 5 ) = 12 2) 84 : ( x - 3 ) = 42
х + 5 = 12 : 2 х - 3 = 84 : 42
х + 5 = 6 х - 3 = 2
х = 6 - 5 х = 2 + 3
х = 1 х = 5
проверка: проверка:
2 * ( 1 + 5 ) = 2 * 6 = 12 84 : ( 5 - 3 ) = 84 : 2 = 42
3) 3 * ( x + 4 ) = 33 4) 45 : ( x - 5 ) = 15
х + 4 = 33 : 3 х - 5 = 45 : 15
х + 4 = 11 х - 5 = 3
х = 11 - 4 х = 3 + 5
х = 7 х = 8
проверка: проверка:
3 * ( 7 + 4 ) = 3 * 11 = 33 45 : ( 8 - 5 ) = 45 : 3 = 15
5) 4 * ( x - 7 ) = 12 6) 6 * ( x - 2 ) = 24
х - 7 = 12 : 4 х - 2 = 24 : 6
х - 7 = 3 х - 2 = 4
х = 3 + 7 х = 4 + 2
х = 10 х = 6
проверка: проверка:
4 * ( 10 - 7 ) = 4 * 3 = 12 6 * ( 6 - 2 ) = 6 * 4 = 24
7) ( x + 3 ) * 3 = 27 8) ( x - 4 ) : 5 = 7
х + 3 = 27 : 3 х - 4 = 7 * 5
х + 3 = 9 х - 4 = 35
х = 9 - 3 х = 35 + 4
х = 6 х = 39
проверка: проверка:
( 6 + 3 ) * 3 = 9 * 3 = 27 ( 39 - 4 ) : 5 = 35 : 5 = 7
9) ( x - 3 ) : 2 = 12 10) ( x - 9 ) * 3 = 12
х - 3 = 12 * 2 х - 9 = 12 : 3
х - 3 = 24 х - 9 = 4
х = 24 + 3 х = 4 + 9
х = 27 х = 13
проверка: проверка:
( 27 - 3 ) : 2 = 24 : 2 = 12 ( 13 - 9 ) * 3 = 4 * 3 = 12
11) ( 3 x + 7 ) * 2 = 32 12) ( 2x - 20 ) : 32 = 6
3х + 7 = 32 : 2 2х - 20 = 6 * 32
3х + 7 = 16 2х - 20 = 192
3х = 16 - 7 2х = 192 + 20
3х = 9 2х = 212
х = 9 : 3 х = 212 : 2
х = 3 х = 106
проверка: проверка:
( 3 * 3 + 7 ) * 2 = 16 * 2 = 32 (2 * 106-20) :32 = 192:32 = 6
13) ( 42 + 2x ) : 2 = 32 14) ( 5x - 7 ) * 5 = 15
42 + 2х = 32 * 2 5х - 7 = 15 : 5
42 + 2х = 64 5х - 7 = 3
2х = 64 - 42 5х = 3 + 7
2х = 22 5х = 10
х = 22 : 2 х = 10 : 5
х = 11 х = 2
проверка: проверка:
( 42 + 2 * 11 ) : 2 = 64 : 2 = 32 ( 5 * 2 - 7 ) * 5 = 3 * 5 = 15
15) ( 13 - 2x ) * 3 = 27 16) ( 40 - 4x ) : 2 = 16
13 - 2х = 27 : 3 40 - 4х = 16 * 2
13 - 2х = 9 40 - 4х = 32
2х = 13 - 9 4х = 40 - 32
2х = 4 4х = 8
х = 4 : 2 х = 8 : 4
х = 2 х = 2
проверка: проверка:
( 13 - 2 * 2 ) * 3 = 9 * 3 = 27 ( 40 - 4 * 2 ) : 2 = 16
17) ( 63 - 9x ) : 3 = 15 18) 4 * ( x - 3 ) = 12
63 - 9х = 15 * 3 х - 3 = 12 : 4
63 - 9х = 45 х - 3 = 3
9х = 63 - 45 х = 3 + 3
9х = 18 х = 6
х = 18 : 9
х = 2
проверка: проверка:
( 63 - 9 * 2 ) : 3 = 45 : 3 = 15 4 * ( 6 - 3 ) = 4 * 3 = 12
19) 5 * ( x + 5 ) = 45 20) 3 * ( x - 7 ) = 9
х + 5 = 45 : 5 х - 7 = 9 : 3
х + 5 = 9 х - 7 = 3
х = 9 - 5 х = 3 + 7
х = 4 х = 10
проверка: проверка:
5 * ( 4 + 5 ) = 5 * 9 = 45 3 * ( 10 - 7 ) = 3 * 3 = 9
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∠ABC = 180° - 120° = 60° (сумма смежных углов равна 180°).
∠BAC = 90° - ∠ABC = 90° - 60° = 30°
Против угла 30° катет в два раза меньше гипотенузы, т.е.
BC = AB/2 = 18/2 = 9
ответ: 9.