Bonjour,
a) 5(x + 2) = 6(2x - 7)
5x + 10 = 12x - 42
5x - 12x = -42 - 10
-7x = -52
[tex]x=\dfrac{-52}{-7}=\dfrac{52}{7}[/tex]
Preuve :
[tex]5\times (\dfrac{52}{7}+2})=5\times (\dfrac{52}{7}+\dfrac{14}{7})=5\times (\dfrac{66}{7})=\dfrac{330}{7}[/tex]
[tex]6\times (2\times\dfrac{52}{7}-7})=6\times (\dfrac{104}{7}-\dfrac{49}{7})=6\times (\dfrac{55}{7})=\dfrac{330}{7}[/tex]
b) -3(3 - x) = 4(3x - 6)
-9 + 3x = 12x - 24
3x - 12x = -24 + 9
-9x = -15
[tex]x=\dfrac{-15}{-9}=\dfrac{5}{3}[/tex]
Preuve :
[tex]-3\times (3-\dfrac{5}{3}})=-3\times (\dfrac{9}{3}-\dfrac{5}{3})=-3\times (\dfrac{4}{3})=-4[/tex]
[tex]4\times (3\times\dfrac{5}{3}-6})=4\times (5-6)=4\times (-1)=-4[/tex]
c) 4x(x - 2) = 4x² + 6x - 8
4x² - 8x = 4x² + 6x - 8
4x² - 4x² - 8x - 6x = -8
-14x = -8
[tex]x=\dfrac{-8}{-14}=\dfrac{4}{7}[/tex]
Preuve :
[tex]4\times \dfrac{4}{7}\times(\dfrac{4}{7}-2)=\dfrac{16}{7}\times(\dfrac{4}{7}-\dfrac{14}{7})=\dfrac{16}{7}\times(-\dfrac{10}{7})=-\dfrac{160}{49}[/tex]
[tex]4\times (\dfrac{4}{7})^2+6\times \dfrac{4}{7}-8= 4\times \dfrac{16}{49}+\dfrac{24}{7}-8= \dfrac{64}{49}+\dfrac{168}{49}-\dfrac{392}{49}=-\dfrac{160}{49}[/tex]
d) (5x + 2)(4x - 3) =20x² - 6x + 40
20x² - 15x + 8x - 6 = 20x² - 6x + 40
20x² - 20x² - 15x + 8x + 6x = 40 + 6
-x = 46
x = -46
Preuve :
[tex][5\times (-46) + 2].[4\times (-46) - 3] = (-230 +2) (-184-3)\\ = (-228)\times (-187) = 42636.[/tex]
[tex]20\times (-46)^2 - 6\times (-46) + 40 = 20\times 2116 + 276 +40 \\= 42320+276+40 = 42636[/tex]
e) (4 - 3x)(5x + 8) = 38 - 15x²
20x + 32 - 15x² - 24x = 38 - 15x²
20x - 24x - 15x² + 15x² = 38 - 32
-4x = 6
[tex]x=\dfrac{6}{-4}=-\dfrac{3}{2}[/tex]
Preuve :
[tex][4-3\times (-\dfrac{3}{2})][5\times (-\dfrac{3}{2})+8] = [4+\dfrac{9}{2}][ (-\dfrac{15}{2})+8]\\ = [\dfrac{8}{2}+\dfrac{9}{2}][ (-\dfrac{15}{2})+\dfrac{16}{2}] = \dfrac{17}{2}\times \dfrac{1}{2}] =\dfrac{17}{4}[/tex]
[tex]38 - 15\times (-\dfrac{3}{2})^2=38-15\times \dfrac{9}{4} = \dfrac{152}{4}-\dfrac{135}{4}= \dfrac{17}{4}[/tex]
