Question

7 Résoudre les équations d'inconnue x suivantes:

a.-2x + 7 = -x +9
c.4x +15=2x+6
b. 8x+26=5x+14
d. 7x+31= 16x +17

Answer 1

A)

`\sf -2x+7=-x+9`

`\sf -2x+7-7=-x+9-7`

`\sf -2x=-x+2`

`\sf -2x+x=-x+2+x`

`\sf -x=2`

`\sf \cfrac{-x}{-1}=\cfrac{2}{-1}`

`\boxed{\sf x=-2}`

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B)

`\sf 4x +15=2x+6`

`\sf 4x+15-15=2x+6-15`

`\sf 4x=2x-9`

`\sf 4x-2x=2x-9-2x`

`\sf 2x=-9`

`\sf \cfrac{2x}{2}=\cfrac{-9}{2}`

`\boxed{\sf x=-\cfrac{9}{2}}`

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C)

`\sf 8x+26=5x+14`

`\sf 8x+26-26=5x+14-26`

`\sf 8x=5x-12`

`\sf 8x-5x=5x-12-5x`

`\sf 3x=-12`

`\sf \cfrac{3x}{3}=\cfrac{-12}{3}`

`\boxed{\sf x=-4}`

____________________

D)

`\sf 7x+31=16x+17`

`\sf 7x+31-31=16x+17-31`

`\sf 7x=16x-14`

`\sf 7x-16x=16x-14-16x`

`\sf -9x=-14`

`\sf \cfrac{-9x}{-9}=\cfrac{-14}{-9}`

`\boxed{\sf x=\cfrac{14}{9}}`