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Pour les mathématiciens, la notion d'équation permet d'instaurer un ordre entre les divers entités qui compose les mathématiques.

Exercices de mathsModifier

Equations avec fractionsModifier

On peut aussi rencontrer des équations avec des fractions.

=Modifier

courage;)

RemarquesModifier

Si vous ne savez pas par quel coefficient multiplicateur il faut pour avoir des fractions de même dénominateur, observez bien les dénominateurs. Multipliez entre eux pour avoir le dénominateur maximal et choissez vos coefficiants multplicateurs pour obtenir ce dénominateur. Ainsi, vous pourrez simplifier à la fin de l'équation.

-3x+3/2=5/3+7xModifier

Deuxième exempleModifier

Soit 1-\frac{4x-3}{5}+5x=\frac{3x+5}{4}. Résoudre une équation 86.208.49.182 mai 26, 2012 à 12:43

Dans un problèmeModifier

Un cinéma propose deux abonnements à ces clients. L'abonnement A propose de voir un film à 7,50€ et l'abonnement B propose de payer 20€ avant tout visionnage de film et le film est alors à 4,50€.

Quel est la formule la plus avantageuse si on veut regarde 5, 10 et 15 films ?


Exercices


Exercice 1

Enoncé

Résoudre les équations :<img data-rte-meta="%7B%22type%22%3A%22double-brackets%22%2C%22lineStart%22%3A%221%22%2C%22title%22%3A%22une%20%5Cu00e9toile%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%7B%7Bune%20%5Cu00e9toile%7D%7D%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-double-brackets" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="double-brackets" />
1


a.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E5x-9%3D4x%2B2%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />b.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E4x-19%3D2%282%2B3x%29%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />c.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E7%2B2%284x-2%29%3D14-4x%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />
<img data-rte-meta="%7B%22type%22%3A%22double-brackets%22%2C%22lineStart%22%3A%221%22%2C%22title%22%3A%22une%20%5Cu00e9toile%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%7B%7Bune%20%5Cu00e9toile%7D%7D%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-double-brackets" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="double-brackets" />
2


a.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E4x%2B3%285x%2B4%29%3D2x-12%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />b.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E5x-5%283-2x%29%3D4-%282x-7%29%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />c.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E3x-5%283-2x%29%3D6x-15%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />
<img data-rte-meta="%7B%22type%22%3A%22double-brackets%22%2C%22lineStart%22%3A%221%22%2C%22title%22%3A%22deux%20%5Cu00e9toiles%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%7B%7Bdeux%20%5Cu00e9toiles%7D%7D%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-double-brackets" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="double-brackets" />
3


a.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E4%28x-2%29-3%5B6-2%283-4x%29%5D%2B3%287-2x%29%3D0%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />b.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E2%284-6x%29-5%5B3-%284-3x%29%5D%3D4%282x-1%29%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />c.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E4x-%5B8-4%283-4x%29%5D%3D6-2%5B4-%287-2x%29%5D%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" /><img data-rte-meta="%7B%22type%22%3A%22double-brackets%22%2C%22lineStart%22%3A%221%22%2C%22title%22%3A%22deux%20%5Cu00e9toiles%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%7B%7Bdeux%20%5Cu00e9toiles%7D%7D%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-double-brackets" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="double-brackets" />
4


a.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E%20%5C%5Cfrac%7B4x-2%7D%7B9%7D-%5C%5Cfrac%7Bx%7D%7B6%7D%3D%20%5C%5Cfrac%7B14-2x%7D%7B3%7D%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />b.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E%20%5C%5Cfrac%7B8x-5%7D%7B4%7D-%5C%5Cfrac%7Bx-7%7D%7B8%7D%3D%20%5C%5Cfrac%7B4-2x%7D%7B12%7D%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />
c.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E%20%5C%5Cfrac%7Bx-9%7D%7B3%7D-%5C%5Cfrac%7Bx%7D%7B6%7D%3D%209-2%282x%2B5%29%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />



<img data-rte-meta="%7B%22type%22%3A%22double-brackets%22%2C%22lineStart%22%3A%221%22%2C%22title%22%3A%22trois%20%5Cu00e9toiles%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%7B%7Btrois%20%5Cu00e9toiles%7D%7D%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-double-brackets" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="double-brackets" />
5


a.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E3-%5C%5Cfrac%7B1%7D%7B2%7D%28%5C%5Cfrac%7B3-4x%7D%7B2%7D-3%29%2B%5C%5Cfrac%7Bx-5%7D%7B3%7D%3D%205x%2B%287-2x%29%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />
b.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E%20%5C%5Cfrac%7B%5C%5Cfrac%7B2x-3%7D%7B2%7D%7D%7B%5C%5Cfrac%7B3%7D%7B4%7D%7D-%5C%5Cfrac%7Bx%7D%7B6%7D%3D%20%5C%5Cfrac%7B3%7D%7B5%7D%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />



c.<img data-rte-meta="%7B%22type%22%3A%22ext%22%2C%22placeholder%22%3A1%2C%22wikitext%22%3A%22%3Cmath%3E%201-%5C%5Cfrac%7B1%7D%7B4%7D%28%5C%5Cfrac%7B4x-2%7D%7B9%7D-%5C%5Cfrac%7Bx%7D%7B6%7D%29%3D4x-1-%20%5C%5Cfrac%7B2x%2B8%7D%7B3%7D%3C%5C%2Fmath%3E%22%7D" data-rte-instance="1792-18320607414f3906cfd786d" class="placeholder placeholder-ext" src="data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D" type="ext" />



Commentaires avant de lire la correction

La première et la deuxième séries d'équations ne posent aucun preoblème car ce n'est juste qu'une application de cours. Ce qui devient plus complexe, ce sont les suivantes. Dans la troisième série d'équations, par exemple, il faut développer tous les termes entre parenthèses puis réduire au maximum l'équation donnée.Dans la quatrième série, attention, on utilise des fractions dans l'équation. Il faut faire en sorte que toutes les fractions présentes dans l'équation aient le même dénominateur. On peut alors supprimer les dénominateurs pour ensuite calculer les numérateurs entre eux.La cinquième série est assez difficile car elle mélange la difficulté de la troisième et quatrième série. Il faut tout d'abord développer les expressions au maximum et ensuite, mettre les fractions avec les même dénominateurs. Attention aux erreurs de calculs qui peuvent se multiplier si vous ne faites pas attention aux coefficiants multiplicateurs.Bon courage !

Solutions

<img 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