Question

ayudenme porfavor les dare una corona los que no saben resolver no resuelvan ​

Answer 1

Respuesta:

1.)

$3x-2<1\\\\3x-2+2<1+2\\\\3x<3\\\\\frac{3x}{3}<\frac{3}{3}\\\\x<1$

2.)

$-2x+1\le \:x-3\\\\-2x+1-1\le \:x-3-1\\\\-2x\le \:x-4\\\\-2x-x\le \:x-4-x\\\\-3x\le \:-4\\\\\left(-3x\right)\left(-1\right)\ge \left(-4\right)\left(-1\right)\\\\3x\ge \:4\\\\\frac{3x}{3}\ge \frac{4}{3}\\\\x\ge \frac{4}{3}$

3.)

$\frac{x-1}{4}<\frac{x+3}{3}-\frac{x-5}{2}\\\\\frac{x-1}{4}\cdot \:12<\frac{x+3}{3}\cdot \:12-\frac{x-5}{2}\cdot \:12\\\\3\left(x-1\right)<4\left(x+3\right)-6\left(x-5\right)\\\\3x-3<-2x+42\\\\3x-3+3<-2x+42+3\\\\3x<-2x+45\\\\3x+2x<-2x+45+2x\\\\5x<45\\\\\frac{5x}{5}<\frac{45}{5}\\\\x<9$

4.)

$-4x\le \:-3x-5\\\\\mathrm{Sumamos\:}3x\mathrm{\:a\:ambos\:lados}\\\\-4x+3x\le \:-3x-5+3x\\\\\mathrm{Simplificamos}\\\\-x\le \:-5\\\\\mathrm{Multiplicamos\:ambos\:lados\:por\:-1\:\left(invierte\:la\:desigualdad\right)}\\\\\left(-x\right)\left(-1\right)\ge \left(-5\right)\left(-1\right)\\\\\mathrm{Simplificamos}\\\\x\ge \:5$

5.)

$2x-5<3x-6\\\\\mathrm{Sumamos\:}5\mathrm{\:a\:ambos\:lados}\\\\2x-5+5<3x-6+5\\\\\mathrm{Simplificamos}\\\\2x<3x-1\\\\\mathrm{Restamos\:}3x\mathrm{\:de\:ambos\:lados}\\\\2x-3x<3x-1-3x\\\\\mathrm{Simplificamos}\\\\-x<-1\\\\\mathrm{Multiplicamos\:ambos\:lados\:por\:-1\:\left(invierte\:la\:desigualdad\right)}\\\\\left(-x\right)\left(-1\right)>\left(-1\right)\left(-1\right)\\\\\mathrm{Simplificamos}\\\\x>1$

Rta: 5 si pertenece al conjunto de la solución de $2x-5<\:3x-6$.

6.)

$3x-7>x+5\\\\3x-7+7>x+5+7\\\\3x>x+12\\\\3x-x>x+12-x\\\\2x>12\\\\\frac{2x}{2}>\frac{12}{2}\\\\x>6\\\\grafica\al\final$

7.)

$\frac{3x+1}{7}-\frac{2-4x}{3}<\frac{-5x-4}{14}+\frac{7x}{6}\\\\\frac{3x+1}{7}\cdot \:42-\frac{2-4x}{3}\cdot \:42<\frac{-5x-4}{14}\cdot \:42+\frac{7x}{6}\cdot \:42\\\\6\left(3x+1\right)-14\left(-4x+2\right)<3\left(-5x-4\right)+49x\\\\74x-22<34x-12\\\\74x-22+22<34x-12+22\\\\74x<34x+10\\\\74x-34x<34x+10-34x\\\\40x<10\\\\\frac{40x}{40}<\frac{10}{40}\\\\x<\frac{1}{4}$

espero que te ayude

#yoaprendi