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8/16/2019 Ecuaciones Sin Denominadores 1º ESO
1/5
IES “Los Colegiales” Matemáticas 1º ESO Tema 6 Lenguaje Algebraico Ecuaciones
Ecuaciones de Primer Grado con una incógnita sin denominadores
1) 2 x + 1 = 21
2) 7 = x + 3
3) 8 x – 5x = x + 8
4) 3 x = 9 x + 12
5) 3 x + = 2 x + 13
) 5 x – 7 = 2 – 4 x
7) 5 x – 8 + 2 x = 7 + 4 x – 9
8) 3 x + x + 4 = 2 x + 3!
9) 4 x + 7 – x = 5 + 2 x
1!) 4 – 2x + 13 = 1! – 9x + 7
11) 7 x – 1! + x – 2 = x – 3 + 3x – 1
12) 5 x – 7 + 2 x = 3 x – 3 + 4 x – 5 + x
13) "x – 5 ) – " 4 x + 7 ) = + 3 x
14) 13 – " x + 5 ) = 4 x – " x – 5 )
15) 3 " 4 x – 1 ) – 2 " 5 x – 3 ) + 3x = – 11 – 2x
1) 7 x – 2 " 5 – x ) = 3 + 2 x + 1
17) 3 " x – 2 ) – 5 " 2 x – 1 ) + 2 " 3 x + 4 ) + 1! = – x
18) 5 x – 3 " 2 x – 1 ) = 1 – 4 " x – 2 )
19) 3 " 4x – 1 ) – 2 "5x – 3 ) = 11 – 2x + 1
2!) 5 " 2 – 2x ) + 3 " x – ) = 1 – 4 " + 2x) + x
21) " 2 x – 1 ) – " x – 7 ) = 2
22) 3 " 3 x – 2 ) – 7 x – 1 = " 2 x – 7 ) – 15 x
!co "a#ier Sánc$e% &arc'a (ág 1)*
8/16/2019 Ecuaciones Sin Denominadores 1º ESO
2/5
IES “Los Colegiales” Matemáticas 1º ESO Tema 6 Lenguaje Algebraico Ecuaciones
#eso$ución de Ecuaciones sin denominadores
1) 2 x + 1 = 21
2 x = 21 – 1
2 x = 2!
x = 2!
2
2) 7 = x + 3
– x = 3 – 7
– x = – 4
x = 4
3) 8 x – 5x = x + 8
8 x – 5x – x = 8
2x = 8
x = 8
2
4) 3 x = 9 x + 12
3 x – 9x = 12
– x = 12
x = 12
–
5) 3 x + = 2 x + 13
3x – 2x = 13 –
x = 7
) 5 x – 7 = 2 – 4 x
5x + 4x = 2 + 7
9x = 9
x = 99
!co "a#ier Sánc$e% &arc'a (ág +)*
x = 10
x = 4
x = 4
x = - 2
x = 7
x = 1
8/16/2019 Ecuaciones Sin Denominadores 1º ESO
3/5
IES “Los Colegiales” Matemáticas 1º ESO Tema 6 Lenguaje Algebraico Ecuaciones
7) 5 x – 8 + 2 x = 7 + 4 x – 9
5x + 2x – 4x = 7 – 9 + 8
3x =
x =
3
8) 3 x + x + 4 = 2 x + 3!
3 x + x – 2x = 3! – 4
2x = 2
x = 2
2
9) 4 x + 7 – x = 5 + 2 x
4 x – x – 2x = 5 – 7
x = – 2
1!) 4 – 2x + 13 = 1! – 9x + 7
– 2x + 9x = 1! + 7 – 4 – 13
7x = !
x = !
7
11) 7 x – 1! + x – 2 = x – 3 + 3x – 1
7 x + x – x – 3x = – 3 – 1 + 1! + 2
– x = 8
x = – 8
12) 5 x – 7 + 2 x = 3 x – 3 + 4 x – 5 + x
5 x + 2x – 3x – 4x – x = – 3 – 5 + 7
– x = – 1
x = 1
!co "a#ier Sánc$e% &arc'a (ág ,)*
x = 2
x = 13
x = - 2
x = 0
x = - 8
x = 1
8/16/2019 Ecuaciones Sin Denominadores 1º ESO
4/5
IES “Los Colegiales” Matemáticas 1º ESO Tema 6 Lenguaje Algebraico Ecuaciones
13) "x – 5 ) – " 4 x + 7 ) = + 3 x
x – 5 – 4x – 7 = + 3x
x – 4x – 3x = + 5 + 7
– x = 18
x = 18
–
14) 13 – " x + 5 ) = 4 x – " x – 5 )
13 – x – 5 = 4 x – x + 5
– x – 4 x + x = 5 – 13 + 5
x = – 3
15) 3 " 4 x – 1 ) – 2 " 5 x – 3 ) + 3x = – 11 – 2x
12x – 3 – 1!x + + 3x = – 11 – 2x
12x – 1!x + 3x + 2x = – 11 + 3 –
7x = – 14
x = – 14
7
1) 7 x – 2 " 5 – x ) = 3 + 2 x + 8
7x – 1! + 2x = 3 + 2x + 8
7x + 2x – 2x = 3 + 8 + 1!
7x = 21
x = 21
7
17) 3 " x – 2 ) – 5 " 2 x – 1 ) + 2 " 3 x + 4 ) + 1! = – x
3x – – 1!x + 5 + x + 8 + 1! = – x
3x – 1!x + x + x = – 5 – 8 – 1!
!x = – 17
%o tiene so$ución &or'ue ning(n n mu$ti&$icado &or ! da – 17
!co "a#ier Sánc$e% &arc'a (ág -)*
x = - 3
x = - 3
x = - 2
x = 3
x = no tiene solución
8/16/2019 Ecuaciones Sin Denominadores 1º ESO
5/5
IES “Los Colegiales” Matemáticas 1º ESO Tema 6 Lenguaje Algebraico Ecuaciones
18) 5 x – 3 " 2 x – 1 ) = 1 – 4 " x – 2 )
5x – x + 3 = 1 – 4x + 8
5x – x + 4x = 1 + 8 – 3
3x =
x =
3
19) 3 " 4x – 1 ) – 2 "5x – 3 ) = 11 – 2x + 1
12x – 3 – 1!x + = 11 – 2x + 1
12x – 1!x + 2x = 11 + 1 + 3 –
4x = 24
x = 24
4
2!) 5 " 2 – 2x ) + 3 " x – ) = 1 – 4 " + 2x) + x
1! – 1!x + 3x – 18 = 1 – 24 – 8x + x
– 1!x + 3x + 8x – x = 1 – 24 – 1! + 18
!x = !
*ua$'uier n cum&$e $a igua$dad
21) " 2 x – 1 ) – " x – 7 ) = 2
2x – 1 – x + 7 = 2
2x – x = 2 + 1 – 7
x = – 4
22) 3 " 3 x – 2 ) – 7 x – 1 = " 2 x – 7 ) – 15 x
9x – – 7x – 1 = 12x – 42 – 15x
9x – 7x – 12x + 15x = – 42 + + 1
5x = – 35
x = – 35
5
!co "a#ier Sánc$e% &arc'a (ág *)*
x = 2
x = 6
Es una identidad
x = - 4
x = - 7