Respuesta:
x < - 23
Explicación paso a paso:
Formula : -
( a + b ) ( a + c ) = a^2 + ( b + c )a + ac
( x + 3 ) ( x - 4 )
= x^2 + ( 3 + ( - 4 ) )x + ( 3 ) ( - 4 )
= x^2 + ( 3 - 4 )x + ( - 12 )
= x^2 + ( - 1x ) + ( - 12 )
= x^2 - x - 12
( x + 5 ) ( x - 7 )
= x^2 + ( 5 + ( - 7 ) )x + ( 5 ) ( - 7 )
= x^2 + ( 5 - 7 )x + ( - 35 )
= x^2 + ( - 2x ) + ( - 35 )
= x^2 - 2x - 35
( x + 3 ) ( x - 4 ) < ( x + 5 ) ( x - 7 )
x^2 - x - 12 < x^2 - 2x - 35
x^2 - x - 12 - x^2 + 2x + 35 < 0
x^2 - x^2 - x + 2x + 35 - 12 < 0
0 + x + 23 < 0
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Respuesta:
x < - 23
Explicación paso a paso:
Formula : -
( a + b ) ( a + c ) = a^2 + ( b + c )a + ac
( x + 3 ) ( x - 4 )
= x^2 + ( 3 + ( - 4 ) )x + ( 3 ) ( - 4 )
= x^2 + ( 3 - 4 )x + ( - 12 )
= x^2 + ( - 1x ) + ( - 12 )
= x^2 - x - 12
( x + 5 ) ( x - 7 )
= x^2 + ( 5 + ( - 7 ) )x + ( 5 ) ( - 7 )
= x^2 + ( 5 - 7 )x + ( - 35 )
= x^2 + ( - 2x ) + ( - 35 )
= x^2 - 2x - 35
( x + 3 ) ( x - 4 ) < ( x + 5 ) ( x - 7 )
x^2 - x - 12 < x^2 - 2x - 35
x^2 - x - 12 - x^2 + 2x + 35 < 0
x^2 - x^2 - x + 2x + 35 - 12 < 0
0 + x + 23 < 0
x < - 23