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[apunts-espa-matematiques.git] / ng-algebra-equacions-primer-grau.conTeXt

\startsection[reference=seccio:equacions-de-primer-grau, title={Equacions de primer grau}]

\startsubject[title={Preguntes}]

\startexercici[reference=exercici:equacions-senzilles-1-nou, title={senzilles}] Resoleu aquestes equacions:
\startitemize[a, columns, three]
\item $2x + 3 = 5$
\item $5x - 10 = 20$
\item $4x - 5 = 6$
\item $2x - 8 = 4$
\item $7x = 49$
\item $2 = 8x - 1$
\item $10 = 2x - 24$
\item $-3x + 4 = 13$
\item $2x = 10 - 5$
\item $10 = 4x - 2$
\item $5x - 2 = 20$
\item $-8 = -2x -4$
\stopitemize
\stopexercici

\startexercici[reference=exercici:equacions-senzilles-2-nou, title={estàndard}] Resoleu les equacions següents:
\startitemize[a, columns, three]
\item $x = 2 - 5x$
\item $2x = -5x -7$
\item $6x - 7 = 2x$
\item $8x - 8 = 8$
\item $2x = x$
\item $x + x = x+1$
\item $3x - 5x = 2x - 7$
\item $2 = 3x - 5 + 2x$
\item $40 - x = 2x + 2$
\item $-2 - 2x = -x + 7x$
\item $x-2 = 2x - 4$
\item $2x + 8 = -x - 2x$
\item $3x + 5 = 7x - 2$
\item $x - 10 = 2x - 4x + 2$
\item $x - 2 = 4x + 5$
\item $7x - 8 = 5x + 2$
\item $3x - 8 = 7x + 10$
\item $-8 + 4x = 7 - x$
\stopitemize
\stopexercici

\startexercici[reference=exercici:equacions-senzilles-3-nou, title={estàndard}] Resoleu les equacions següents:
\startitemize[a, columns]
\item $5x - 2 + 8x = 2x$
\item $2 = - 2x + 8 - x$
\item $-22x - 2 = -55 + 8x$
\item $x = - 5 - x - 2x$
\item $10x - 20 = 8x - 2x$
\item $42x - 2 = -6 - 3x$
\item $50 - 2x = 8x - 20$
\item $3x - 0.5 = 5x - 2.4$
\item $-3x = - 202 - 8x + 2002$
\item $0 = 2x + 2 + 8x + 2x$
\item $25x - 22 + 28x - 22x = 0$
\item $10x - 20 + 8x = 2$
\item $5 = x - 2 - 7x$
\item $10x - 2 = -5x - 20$
\item $-15x = 2 - 8x$
\item $10x = -2 + 8 + 2x$
\item $10x - 2x + 8 = 2$
\item $5t - 2t = 8t - 2$
\stopitemize
\stopexercici

\startexercici[reference=exercici:equacions-parentesis-1, title={amb parèntesis}] Resoleu les equacions següents:
\startitemize[a, columns]
\item $3 (x - 2) = 5x -2$
\item $5x  = 4 - (x-2)$
\item $3(x-2) = 4(x-3)$
\item $x  = 100 - (x+1)$
\item $x-(2x - 2) = 3$
\item $4x - (x+4) = 40$
\item $9 - (5-2x) = x + 1$
\item $7 -3 (2x-5) = 10$ 
% aqui
\item $5 - 3(2x-4) = x$
\item $4-(5-x) = 2(x + 10)$
\item $x-(x-1) = 1-(1-x)$
\item $2x + 1 = 2 (x+1)$
\item $2(x-4) = 6-(-2x+2)$
\item $-2(4-x) = 2(4-x)$
\item $-9 (-9 + 9x) = 2$
\item $6x = 6(x+1) + 1$
\item $5-(x-1) = 2x$
\item $10-(-x-2) = 5$
\item $2(x-1) + 2x = 0$
\item $-5(-3x-2) = 2(x-1)$
\item $-8(-2x-3) = -5x$
\item $7(2x-3) = 3-(x-1)$
\item $2(x-5) = -2x - 5$
\item $8-(8-x) = 2x -5$
\item $8 = 5 - 2(5-2x)$
\item $7+7(-2x-2)=8$
\item $5-2(x-2) = 6x$
\item $0,5(x-1) = 3(x-2)$
\item $4-(2x-5) = 8(2x)$
\item $-2(8x-2) = 0,5x$
\item $2(5-4x) = -4(x-2)$
\item $5 - 2(x-2) = 5x$
\stopitemize
\stopexercici

\startexercici[reference=exercici:equacions-fraccions-1, title={amb fraccions}] Resoleu les equacions següents:
\startitemize[a, columns]

\item 
\startformula
\frac{x}{2} + 30 = 2x
\stopformula 

\item
\startformula
x-1 = \frac{3x}{4}
\stopformula

\item 
\startformula
x-20 = \frac{x}{3} + 2
\stopformula

\item
\startformula
\frac{2x}{3}-1 = x - \frac{3x}{4} + 4
\stopformula

\item
\startformula
\frac{x}{2} -2 = \frac{x}{4} + 13
\stopformula

\item 
\startformula
2+\frac{x}{3} = \frac{2x}{3} -4
\stopformula

\column
\item
\startformula
\frac{x}{3}+ 4 - \frac{x}{2} = -10
\stopformula

\item
\startformula
\frac{2x}{6} - \frac{2x}{15} = x - 2
\stopformula

\item 
\startformula
\frac{x}{4} + 5 = \frac{7x}{12}
\stopformula 

\item
\startformula
\frac{x}{2} + 2 = 5 - \frac{5x}{6}
\stopformula

\item
\startformula
\frac{x}{2} - \frac{2x}{3} = \frac{4x}{5} + 1
\stopformula

\item
\startformula
\frac{2x}{3} + \frac{3x}{4} = 5x - \frac{2}{3}
\stopformula

\stopitemize
\stopexercici

\startexercici[reference=exercici:equacions-fraccions-1, title={amb fraccions}] TODO: copiar algunes equacions de Alfonso González
\stopexercici

\startexercici[reference=exercici:equacions-fraccions-compostes-1, title={amb fraccions compostes}] TODO: copiar algunes equacions de Alfonso González
\stopexercici


\stopsubject

\page[yes]
\startsubject[title={Solucions}]

Les solucions estan en forma de fracció i simplificades.

\startitemize[1][distance=0.5cm]
\sym{\in[exercici:equacions-senzilles-1-nou]} \startitemize[a, text] \item $x=1$, \item $x=6$, \item $x=11/4$, \item $x=6$, \item $x=7$, \item $x=3/8$, \item $x=17$, \item $x=-3$, \item $x=5/2$, \item $x=3$, \item $x=22/5$, \item $x=2$ \stopitemize

\sym{\in[exercici:equacions-senzilles-2-nou]} \startitemize[a, text] \item $x=1/3$, \item $x=-1$, \item $x=7/4$, \item $x=2$, \i5 - 2(x-2) = 5xtem $x=0$, \item $x=1$, \item $x=7/4$, \item $x=7/5$, \item $x=-38/3$, \item $x=-1/4$, \item $x=2$, \item $x=-8/5$ \item $x=7/4$, \item $x=4$, \item $x=-7/3$, \item $x=5$, \item $x=-9/2$, \item $x=3$ \stopitemize

\sym{\in[exercici:equacions-senzilles-3-nou]}  \startitemize[a, text] \item $2/11$, \item $2$, \item $53/30$, \item $-5/4$, \item $5$, \item $-4/45$, \item $7$, \item $0.95$, \item $360$, \item $-1/6$, \item $22/31$, \item $11/9$, \item $-7/6$, \item $-6/5$, \item $-2/7$, \item $3/4$, \item $-3/4$, \item $2/5$ \stopitemize

\sym{\in[exercici:equacions-parentesis-1]} \startitemize[a, text] \item $x=-2$, \item $x=1$, \item $x=6$, \item $x=99/2$, \item $x=-1$, \item $x=44/3$, \item $x=-3$, \item $x=2$, \item $17/7$, \item $-21$, \item $1$, \item no té solució, \item no té solució, \item $4$, \item $79/81$, \item no té solució, \item $2$, \item $-7$, \item $1/2$, \item $-12/13$, \item $-8/7$, \item $5/3$, \item $5/4$, \item $5$, \item $13/4$, \item $-15/14$, \item $9/8$, \item $2,2$, \item $1/2$, \item $8/33$, \item $1/2$, \item $9/7$  \stopitemize

\sym{\in[exercici:equacions-fraccions-1]} \startitemize[a, text] \item $x=20$, \item $x=4$,  \item $x=60$, \item $x=12$, \item $x=33$, \item $x=18$, \item $x=84$, \item $x=5/2$, \item $x=15$, \item $9/4$, \item $-30/29$, \item $8/43$ \stopitemize

\stopitemize

\stopsubject

\stopsection