Question

me ayuda porfavor es urgente a resolved esta inecuaciones lineales que es para mañana plisssssss​

Answer 1

Respuesta:

a)

$5x+1<6\\5x<6-1\\5x<5\\x<\frac{5}{5}\\ x<1$

b)

$\frac{x}{y} -2+3x\leq 8-x\\3x+x\leq 8+2\\4x\leq 10\\x\leq\frac{10}{4}$

c)

$\frac{x}{y} x+8\leq 3x+1\\x-3x\leq 1-8\\-2x\leq -7\\x\leq \frac{-7}{-2}\\ x\geq \frac{7}{2}$

d)

$x\geq 6-x\\x+x\geq 6\\2x\geq 6\\x\geq \frac{6}{2}\\ x\geq 3$

e)

$3x-1\leq x-11\\3x-x\geq -11+1\\2x\geq -10\\x\geq \frac{-10}{2} \\x\geq -5$

f)

$5<-9-x\\ x<-9-5\\x<-14$

g)

$2-x<\frac{1}{2}\\-x<\frac{1}{2}-2 \\ -x<-1.5\\x>1.5$

h)

$5(2-3x)>3(2-3x)\\10-15x>6-9x\\-15x+9x>-10+6\\-6x>-4\\x>\frac{-4}{-6}\\ x<\frac{4}{6}$

i)

$2x+\frac{1}{2}\geq 2\\2x\geq 2-\frac{1}{2}\\ 2x\geq 1.5\\x\geq \frac{1.5}{2}$

k)

$1+\frac{x+3}{5}<1-x\\ \frac{x+3}{5}\cdot \:5<-x\cdot \:5\\x+3-3<-5x-3\\x+5x<-5x-3+5x\\\frac{6x}{6}<\frac{-3}{6}\\x<-\frac{1}{2}$

j)

$2x+\frac{1}{2}\geq 2\\2x+\frac{1}{2}-\frac{1}{2}\ge \:2-\frac{1}{2}\\2x\ge \frac{3}{2}\\\frac{2x}{2}\ge \frac{\frac{3}{2}}{2}\\x\ge \frac{3}{4}$

l)

$-2-x<\frac{1}{2}\\ -x<\frac{1}{2}-2\\ -x<-1.5\\x>1.5$

m)

$3(2x-3)\geq 2(x+5)-1\\6x-9+9\ge \:2x+9+9\\6x\ge \:2x+18\\6x-2x\ge \:2x+18-2x\\\frac{4x}{4}\ge \frac{18}{4}\\x\ge \frac{9}{2}$

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