Esercizi sulle equazioni numeriche intere

Esercizio n° 1

Svolgi la seguente equazione.

3(x + 2) – (2x + 1) = 10 – 3 (x – 1) – 4x (1)

Esercizio n° 2

Svolgi la seguente equazione.

2(x – 3) – 5(1 + x) – 1 = x + 2( 1 – x) (-7)

Esercizio n° 3

Svolgi la seguente equazione.

5 + 2(4 – x) + 3 (x-5) = 6(x + 2) – 3(4x – 7) (5)

Esercizio n° 4

Svolgi la seguente equazione.

3x (x – 1) – (1 + x)(-4) = 2x² – (1 – x)(1 + x) + 4 (-1)

Esercizio n° 5

Svolgi la seguente equazione.

5 – [ – (x – 1) – 5(2x – 1) ] =2 + x + 5(2x – 3) (impos)

Esercizio n° 6

Svolgi la seguente equazione.

x – 1 + 5(x – 3) + (-2)² = 6 (x – 2) (indet.)

Esercizio n° 7

Svolgi la seguente equazione.

$\frac{1}{2}$ (1 + 2x) – x + $\frac{2}{5}$ (x + 2) = $\frac{3}{10}$ x – $\frac{1}{2}$ (-18)

Esercizio n° 8

Svolgi la seguente equazione.

2(x – 1)(1 + x) + (2 – x)³ + 12x = 2(2x – 1)(1 + 2x) – x³ + 8 (indet.)

Esercizio n° 9

Svolgi la seguente equazione.

$\frac{1}{2}$ (x – 1) + $\frac{1}{4}$ (x + 1) + x $(\frac{1}{2}- 2)$ = 1 – 2x (1)

Esercizio n° 10

Svolgi la seguente equazione.

(2x – 1) $(\frac{1}{3}- \frac{1}{2})$ + $\frac{1}{2}$ x = 4 + $\frac{x}{6}$ (impos)

Esercizio n° 11

Svolgi la seguente equazione.

$\frac{2x + 1}{10}$ – $\frac{1 - 3x}{5}$ + $\frac{x - 1}{2}$ – 2 = 2(x – 2) (2)

Esercizio n° 12

Svolgi la seguente equazione.

( $\frac{3}{4}$ – 3x) ( $\frac{4}{3}$ – 2x) = 4x (3x + $\frac{1}{2}$ ) – (2x – $\frac{3}{2}$ ) (3x – $\frac{1}{2}$ ) (7\52)

Esercizio n° 13

Svolgi la seguente equazione.

$\frac{2x - 1}{3}(x - \frac{1}{3})- \frac{1}{3}$ [x² + x(x – $\frac{1}{4}$ )] = $\frac{1}{4}$ (x + $\frac{2}{3}$ ) (-1\13)

Esercizio n° 14

Svolgi la seguente equazione.

$\frac{2(x - 1)( x ^{2}+ x + 1)}{5}$ = 3 – 2x + $\frac{(x ^{2}- x + 1)(x + 1)}{3}$ + $\frac{x ^{3}-11}{15}$ (3\2)

Esercizio n° 15

Svolgi la seguente equazione.

$\frac{3x + 2}{5}$ + $\frac{1}{2}$ x – $\frac{1}{5}$ [ x + 2 – $\frac{1}{2}$ (x – $\frac{2}{3}$ )] = $\frac{3x + 1}{10}$ + $\frac{2}{3}$ x (5)

Esercizio n° 16

Svolgi la seguente equazione.

$\frac{1 + x ^{2}}{5}$ – $\frac{1}{4}$ x – $\frac{1}{20}$ = $\frac{(x - 1) ^{2}}{5}$ + $\frac{3}{2}$ – 1 (11\3)

Esercizio n° 17

Svolgi la seguente equazione.

$\frac{x}{10}$ + $\frac{(2 - 3x) ^{2}}{30}$ + $\frac{x}{10}$ (1 – x) + $\frac{2}{15}$ (1 + 5x) = $\frac{x}{5}$ (3 + x) – $\frac{x - 2}{6}$ (2)

Esercizio n° 18

Svolgi la seguente equazione.

$\frac{1}{2}$ [- $\frac{x - 1}{3}$ ( $\frac{1}{2}$ – 2) + $\frac{1 - 2x}{6}$ ] : 3 = 2 ( $\frac{1}{6}$ – $\frac{x}{3}$ ) + $\frac{1}{6}$ (5x – $\frac{1}{6}$ ) + x – $\frac{41}{36}$ x (imposs)

Esercizio n° 19

Svolgi la seguente equazione.

(x – $\frac{1}{4}$ )² – (2x + $\frac{1}{3}$ ) (2x – $\frac{1}{3}$ ) + 5x ( x – $\frac{1}{4}$ ) – $\frac{1}{144}$ = ( x + $\frac{1}{3}$ ) (2x – $\frac{5}{2}$ ) + $\frac{2}{3}$ (-4)

Esercizio n° 20

Svolgi la seguente equazione.

(x – $\frac{1}{3}$ )³ – ( $\frac{2}{5}$ x – 1)(2 – x) – x( $\frac{2}{5}$ x + 3) = x²(x – 1) – $\frac{1}{3}$ (2 – x) – $\frac{1}{27}$ (5\9)

Esercizio n° 21

Svolgi la seguente equazione.

$\frac{2(x + 1) + \frac{1}{2}(x + 2)}{2}$ + $\frac{\frac{x - 2}{3}- \frac{x}{2}}{3}$ = x + $\frac{5}{3}$ (2)

Svolgimento

Esercizio n° 1

Svolgi la seguente equazione.

3(x + 2) – (2x + 1) = 10 – 3 (x – 1) – 4x

3x + 6 – 2x – 1 = 10 – 3x + 3 – 4x

3x – 2x + 3x + 4x = 10 + 3 – 6 + 1

8x =+ 8

x = 1

Esercizio n° 2

Svolgi la seguente equazione.

2(x – 3) – 5(1 + x) – 1 = x + 2( 1 – x)

2x – 6 – 5 – 5x – 1 = x + 2 – 2x

2x – 5x – x + 2x = 2 + 6 + 5 + 1

-2x = 14 $\frac{-2}{-2}x = \frac{14}{-2}$

x = – $\frac{14}{2}$ = -7

Esercizio n° 3

Svolgi la seguente equazione.

5 + 2(4 – x) + 3 (x-5) = 6(x + 2) – 3(4x – 7)

5 + 8 – 2x + 3x – 15 = 6x + 12 – 12x + 21

-2x + 3x – 6x + 12x = 12 + 21 – 5 – 8 + 15

7x = 35 ⇒ $\frac{7}{7}x = \frac{35}{7}$

x = 5

Esercizio n° 4

Svolgi la seguente equazione.

3x (x – 1) – (1 + x)(-4) = 2x² – (1 – x)(1 + x) + 4

3x² – 3x – (-4 – 4x) = 2x² – (1 – x²) + 4

3x² – 3x + 4 + 4x = 2x² – 1 + x² + 4

3x² – 2x² – x² – 3x + 4x = -1 + 4 – 4

x = -1

Esercizio n° 5

Svolgi la seguente equazione.

5 – [ – (x – 1) – 5(2x – 1) ] =2 + x + 5(2x – 3)

5 – ( -x +1 -10x + 5 ) = 2 + x + 10x – 15

5 +x – 1 + 10x – 5 = 2 + x + 10x – 15

x + 10x – x – 10x = 2 – 15 – 5 + 1 + 5

0 = -12 impossibile

Esercizio n° 6

Svolgi la seguente equazione.

x – 1 + 5(x – 3) + (-2)² = 6 (x – 2)

x – 1 + 5x – 15 + 4 = 6x – 12

6x – 6x = -12 + 1 + 15 – 4

0 = 0 indeterminata

Esercizio n° 7

Svolgi la seguente equazione.

$\frac{1}{2}$ (1 + 2x) – x + $\frac{2}{5}$ (x + 2) = $\frac{3}{10}$ x – $\frac{1}{2}$

$\frac{1}{2}$ + ~~x – x~~ + $\frac{2}{5}$ x + $\frac{4}{5}$ = $\frac{3}{10}$ x – $\frac{1}{2}$

$\frac{2}{5}$ x – $\frac{3}{10}$ x = – $\frac{1}{2}$ – $\frac{1}{2}$ – $\frac{4}{5}$

10 · $\frac{4x - 3x}{10}$ = $\frac{- 5 - 5-8}{10}$ · 10

4x – 3x = – 18

x = -18

Esercizio n° 8

Svolgi la seguente equazione.

2(x – 1)(1 + x) + (2 – x)³ + 12x = 2(2x – 1)(1 + 2x) – x³ + 8

2(x² – 1) + 8 + 3 (2)² (-x) + 3(2)(-x)² -x³ + 12x = 2 (4x² – 1) – x³ + 8

2x² ~~– 2~~ ~~+ 8~~ ~~-12x~~ +6x² ~~– x³~~ ~~+ 12x~~ = 8x² ~~– 2~~ ~~– x³~~ ~~+ 8~~

2x² + 6x² = 8x²

8x² – 8x²= 0

0 = 0 indeterminata

Esercizio n° 9

Svolgi la seguente equazione.

$\frac{1}{2}$ (x – 1) + $\frac{1}{4}$ (x + 1) + x $(\frac{1}{2}- 2)$ = 1 – 2x

$\frac{1}{2}$ x – $\frac{1}{2}$ + $\frac{1}{4}$ x + $\frac{1}{4}$ + $\frac{1}{2}$ x ~~– 2x~~ = 1 ~~– 2x~~

$\frac{1}{2}$ x + $\frac{1}{4}$ x + $\frac{1}{2}$ x = + $\frac{1}{2}$ – $\frac{1}{4}$ + 1

4 · $\frac{2x + x + 2x}{4}$ = $\frac{2 - 1 + 4}{4}$ · 4

5x = 5 ⇒ $\frac{5}{5} = \frac{5}{5}$

x = 1

Esercizio n° 10

Svolgi la seguente equazione.

(2x – 1) $(\frac{1}{3}- \frac{1}{2})$ + $\frac{1}{2}$ x = 4 + $\frac{x}{6}$

$\frac{2}{3}$ x – x – $\frac{1}{3}$ + $\frac{1}{2}$ + $\frac{1}{2}$ x = 4 + $\frac{x}{6}$

$\frac{2}{3}$ x – x + $\frac{1}{2}$ x – $\frac{x}{6}$ = 4 + $\frac{1}{3}$ – $\frac{1}{2}$

6 · $\frac{4x -6x +3x -x}{6}$ = $\frac{24 + 2 - 3}{6}$ · 6

0 =23 impossibile

Esercizio n° 11

Svolgi la seguente equazione.

$\frac{2x + 1}{10}$ – $\frac{1 - 3x}{5}$ + $\frac{x - 1}{2}$ – 2 = 2(x – 2)

10 · $\frac{2x + 1 -2(1-3x)+5(x - 1)- 20}{10}$ = $\frac{20(x-2)}{10}$ · 10

2x + 1 – 2 + 6x + 5x – 5 – 20 = 20x – 40

2x + 6x + 5x – 20x = -40 – 1 + 2 + 5 + 20

-7x = -14 ⇒ $\frac{-7}{-7}$ x = $\frac{-14}{-7}$

x = 2

Esercizio n° 12

Svolgi la seguente equazione.

( $\frac{3}{4}$ – 3x) ( $\frac{4}{3}$ – 2x) = 4x (3x + $\frac{1}{2}$ ) – (2x – $\frac{3}{2}$ ) (3x – $\frac{1}{2}$ )

$\frac{3}{4}$ · $\frac{4}{3}$ + $\frac{3}{4}$ · (-2x) – 3x( $\frac{4}{3}$ ) -3x (-2x) = 12x² + 4x ( $\frac{1}{2}$ ) – (6x² -x – $\frac{9}{2}$ x + $\frac{3}{4}$ )

1 – $\frac{6}{4}$ x -4x +6x² = 12x² + 2x -6x² + x + $\frac{9}{2}$ x – $\frac{3}{4}$

– $\frac{6}{4}$ x -4x +6x² – 12x² -2x + 6x² – x – $\frac{9}{2}$ x = – $\frac{3}{4}$ – 1

– $\frac{6}{4}$ x -7x – $\frac{9}{2}$ x = – $\frac{3}{4}$ – 1

4 · $\frac{-6x-28x - 18x }{4}$ = $\frac{-3 - 4}{4}$ · 4

-52x = – 7 ⇒ $\frac{-52 }{-52}$ x = $\frac{-7 }{-52}$

x = $\frac{7 }{52}$

Esercizio n° 13

Svolgi la seguente equazione.

$\frac{2x - 1}{3}(x - \frac{1}{3})- \frac{1}{3}$ [x² + x(x – $\frac{1}{4}$ )] = $\frac{1}{4}$ (x + $\frac{2}{3}$ )

$\frac{ 2x^{2}-x}{3}$ – $\frac{ 2x-1}{9}$ – $\frac{1}{3}$ (x² + x² – $\frac{1}{4}$ x ) = $\frac{1}{4}$ x + $\frac{1}{6}$

$\frac{ 2x^{2}-x}{3}$ – $\frac{ 2x-1}{9}$ – $\frac{1}{3}$ x² – $\frac{1}{3}$ x² + $\frac{1}{12}$ x = $\frac{1}{4}$ x + $\frac{1}{6}$

36 · $\frac{12(2x ^{2}-x)-4(2x - 1)-12x ^{2}-12x ^{2}+3x}{36}$ = $\frac{9x + 6}{36}$ ·36

24x² – 12x – 8x + 4 – 12x² – 12x² + 3x = 9x + 6

24x² – 12x² – 12x² – 12x – 8x + 3x – 9x = 6 -4

-26x = 2 ⇒ $\frac{-26}{-26}$ x = $\frac{-2}{-26}$

x = – $\frac{1}{13}$

Esercizio n° 14

Svolgi la seguente equazione.

$\frac{2(x - 1)( x ^{2}+ x + 1)}{5}$ = 3 – 2x + $\frac{(x ^{2}- x + 1)(x + 1)}{3}$ + $\frac{x ^{3}-11}{15}$

15 · $\frac{6(x - 1)( x ^{2}+ x + 1)}{15}$ = $\frac{45 - 30x+ 5(x ^{2}- x + 1)(x + 1)+x ^{3}-11 }{15}$ · 15 (x-1)(x²+x+1) = x³-1

6(x³-1) = 45 – 30 x + 5(x³ + 1) + x³ – 11 (x+1)(x²-x+1) = x³+1

6x³-6 = 45 – 30 x + 5x³ + 5+ x³ – 11

6x³+ 30 x – 5x³ – x³ = 45 + 5 – 11 + 6

30x = 45 ⇒ $\frac{30}{{30}}$ x = $\frac{45}{{30}}$ semplificando

x = $\frac{3}{{2}}$

Esercizio n° 15

Svolgi la seguente equazione.

$\frac{3x + 2}{5}$ + $\frac{1}{2}$ x – $\frac{1}{5}$ [ x + 2 – $\frac{1}{2}$ (x – $\frac{2}{3}$ )] = $\frac{3x + 1}{10}$ + $\frac{2}{3}$ x

$\frac{3x + 2}{5}$ + $\frac{1}{2}$ x – $\frac{1}{5}$ [ x + 2 – $\frac{1}{2}$ x + $\frac{1}{{3}}$ ] = $\frac{3x + 1}{10}$ + $\frac{2}{3}$ x

$\frac{3x + 2}{5}$ + $\frac{1}{2}$ x – $\frac{1}{5}$ x – $\frac{2}{5}$ + $\frac{1}{10}$ x – $\frac{1}{15}$ = $\frac{3x + 1}{10}$ + $\frac{2}{3}$ x

30 · $\frac{18x+12 +15x-6x-12+3x - 2}{30}$ = $\frac{9x + 3+20x}{30}$ · 30

18x + 15x – 6x + 3x – 9x – 20x = 3 – 12 + 12 + 2

x = 5

Esercizio n° 16

Svolgi la seguente equazione.

$\frac{1 + x ^{2}}{5}$ – $\frac{1}{4}$ x – $\frac{1}{20}$ = $\frac{(x - 1) ^{2}}{5}$ + $\frac{3}{2}$ – 1

20 · $\frac{4(1 + x ^{2})-5x-1}{20}$ = $\frac{4(x - 1) ^{2}+30-20}{20}$ · 20

4 + 4x² — 5x – 1 = 4 (x² – 2x + 1) +10

4 + ~~4x²~~ – 5x – 1 = ~~4x²~~ -8x + 4 + 10

-5x + 8x = 4 + 10 – 4 + 1

3x = 11 ⇒ $\frac{3}{3}$ x = $\frac{11}{3}$

x = $\frac{11}{3}$

Esercizio n° 17

Svolgi la seguente equazione.

$\frac{x}{10}$ + $\frac{(2 - 3x) ^{2}}{30}$ + $\frac{x}{10}$ (1 – x) + $\frac{2}{15}$ (1 + 5x) = $\frac{x}{5}$ (3 + x) – $\frac{x - 2}{6}$

$\frac{x}{10}$ + $\frac{4 - 12x +9x ^{2}}{30}$ + $\frac{x}{10}$ – $\frac{x ^{2}}{10}$ + $\frac{2}{15}$ + $\frac{2}{3}$ x = $\frac{3}{5}$ x + $\frac{x ^{2}}{5}$ – $\frac{x - 2}{6}$

30 · $\frac{3x+4-12x +9 x ^{2}+3x -3x ^{2} +4 + 20x}{30}$ = $\frac{18x+6 x ^{2}-5(x-2)}{30}$ · 30

3x +4 – 12x +9x² +3x – 3x² + 4 + 20x = 18x + 6x² -5x + 10

3x – 12x + ~~9x²~~ + 3x ~~– 3x²~~ + 20x ~~-6x²~~ -18x +5x = + 10 – 4 – 4

x = 2

Esercizio n° 18

Svolgi la seguente equazione.

$\frac{1}{2}$ [- $\frac{x - 1}{3}$ ( $\frac{1}{2}$ – 2) + $\frac{1 - 2x}{6}$ ] : 3 = 2 ( $\frac{1}{6}$ – $\frac{x}{3}$ ) + $\frac{1}{6}$ (5x – $\frac{1}{6}$ ) + x – $\frac{41}{36}$ x

$\frac{1}{2}$ [- $\frac{x - 1}{6}$ + $\frac{2(x - 1)}{3}$ + $\frac{1 - 2x}{6}$ ] : 3 = $\frac{1}{3}$ – $\frac{2}{3}$ x + $\frac{5}{6}$ x – $\frac{1}{36}$ + x – $\frac{41}{36}$ x

$\frac{1}{2}$ [- $\frac{x - 1}{6}$ + $\frac{2x - 2}{3}$ + $\frac{1 - 2x}{6}$ ] : 3 = $\frac{1}{3}$ – $\frac{2}{3}$ x + $\frac{5}{6}$ x – $\frac{1}{36}$ + x – $\frac{41}{36}$ x

( $-\frac{x - 1}{12}$ + $\frac{2x - 2}{6}$ + $\frac{1 - 2x}{12}$ ) · $\frac{1}{3}$ = $\frac{1}{3}$ – $\frac{2}{3}$ x + $\frac{5}{6}$ x – $\frac{1}{36}$ + x – $\frac{41}{36}$ x

( $\frac{-x +1+4x+4+1-2x}{12}$ ) · $\frac{1}{3}$ = $\frac{1}{3}$ – $\frac{2}{3}$ x + $\frac{5}{6}$ x – $\frac{1}{36}$ + x – $\frac{41}{36}$ x

( $\frac{x + 6}{12}$ )· $\frac{1}{3}$ = $\frac{1}{3}$ – $\frac{2}{3}$ x + $\frac{5}{6}$ x – $\frac{1}{36}$ + x – $\frac{41}{36}$ x

$\frac{x + 6}{36}$ = $\frac{1}{3}$ – $\frac{2}{3}$ x + $\frac{5}{6}$ x – $\frac{1}{36}$ + x – $\frac{41}{36}$ x

36 · $\frac{x + 6}{36}$ = $\frac{12 - 24x+30x - 1+36x - 41x}{36}$ · 36

x + 6 = 12 – 24x + 30x – 1 +36x – 41x

x +24x -30x – 36x + 41x = 12 – 1 – 6

0 = 5 impossibile

Esercizio n° 19

Svolgi la seguente equazione.

(x – $\frac{1}{4}$ )² – (2x + $\frac{1}{3}$ ) (2x – $\frac{1}{3}$ ) + 5x ( x – $\frac{1}{4}$ ) – $\frac{1}{144}$ = ( x + $\frac{1}{3}$ ) (2x – $\frac{5}{2}$ ) + $\frac{2}{3}$

x² +2(x)(- $\frac{1}{4}$ )+ $\frac{1}{16}$ – (4x² – $\frac{1}{9}$ ) + 5x² – $\frac{5}{4}x$ – $\frac{1}{144}$ = 2x² – $\frac{5}{2}$ x + $\frac{2}{3}x$ – $\frac{5}{6}$ + $\frac{2}{3}$

x² – $\frac{1}{2}$ x + $\frac{1}{16}$ – 4x² + $\frac{1}{9}$ + 5x² – $\frac{5}{4}x$ – $\frac{1}{144}$ = 2x² – $\frac{5}{2}$ x + $\frac{2}{3}x$ – $\frac{5}{6}$ + $\frac{2}{3}$

x²– $\frac{1}{2}$ x- 4x²+ ~~5x²~~ – $\frac{5}{4}x$ ~~-2x²~~+ $\frac{5}{2}$ x – $\frac{2}{3}x$ = – $\frac{5}{6}$ + $\frac{2}{3}$ – $\frac{1}{16}$ – $\frac{1}{9}$ + $\frac{1}{144}$

144 · $\frac{-72x-180x+360x-96x }{144}$ = $\frac{-120+96-9-16+1}{144}$ · 144

12x = -48 ⇒ $\frac{12}{12}$ x = $-\frac{48}{12}$

x = – 4

Esercizio n° 20

Svolgi la seguente equazione.

(x – $\frac{1}{3}$ )³ – ( $\frac{2}{5}$ x – 1)(2 – x) – x( $\frac{2}{5}$ x + 3) = x²(x – 1) – $\frac{1}{3}$ (2 – x) – $\frac{1}{27}$

x³ +3(x)²( – $\frac{1}{3}$ ) +3(x)( – $\frac{1}{3}$ )² +(- $\frac{1}{3}$ )³ -( $\frac{4}{5}$ x- $\frac{2}{5}$ x² – 2 + x) – $\frac{2}{5}$ x² -3x = x³ – x² – $\frac{2}{3}$ + $\frac{1}{3}$ x – $\frac{1}{27}$

x³ -x² + $\frac{1}{3}$ x – $\frac{1}{27}$ – $\frac{4}{5}$ x + $\frac{2}{5}$ x² +2 – x – $\frac{2}{5}$ x² -3x = x³ – x² – $\frac{2}{3}$ + $\frac{1}{3}$ x – $\frac{1}{27}$

x³ ~~-x²~~ + $\frac{1}{3}$ x – $\frac{4}{5}$ x + ~~$\frac{2}{5}$ x²~~ – x ~~– $\frac{2}{5}$ x²~~ -3x ~~– x³~~ ~~+ x²~~ – $\frac{1}{3}$ x = – $\frac{2}{3}$ – $\frac{1}{27}$ + $\frac{1}{27}$ -2