Bonsoir,
[tex]\\1)\\\\ 2x+3 \leq 3x+8\\
2x-3x\leq 8-3\\
-x\leq 5\\
x\leq -5\\\\[/tex]
[tex]2)\\\\
\dfrac{2x-3}{4}>\dfrac{x+5}{3}\\\\
12\times \dfrac{2x-3}{4}>12\times \dfrac{x+5}{3}\\\\
3(2x-3)>4(x+5)\\
6x-9>4x+20\\
2x> 29\\\\
x>\dfrac{29}{2}\\\\[/tex]
[tex]3)\\\\
\dfrac{x}{2}+3<4x-5\\\\
2\times\dfrac{x}{2}+2\times3<2\times4x-2\times5\\\\
x+6 < 8x-10\\
x-8x<-10-6\\
-7x<-16\\\\
x<\dfrac{16}{7}[/tex]
[tex]4)\\\\
x+\dfrac{1}{4}>3x-\dfrac{3}{5}\\\\
x-3x>-\dfrac{3}{5}-\dfrac{1}{4}\\\\
-2x>-\dfrac{4\times3 + 5\times1}{4\times5}\\\\
-2x > -\dfrac{17}{20}\\\\
x >\dfrac{17}{20}\times \dfrac{1}{2}\\\\\\ x >\dfrac{17}{40}\\\\[/tex]
[tex]5)\\\\
2x-\dfrac{3}{7}\geq \dfrac{x}{3}+\dfrac{2}{5}\\\\
105\times 2x-105\times \dfrac{3}{7}\geq 105\times \dfrac{x}{3}+105\times\dfrac{2}{5}\\\\
210x - 15\times 3 \geq 35x + 21\times 2\\\\
210x - 45\geq 35x+42\\
210x -35x \geq 42+45\\
175x\geq 87\\\\
x\geq \dfrac{87}{175}\\\\[/tex]
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Bonne soirée et bon courage.
