Question

[dân 2k3]

giải các bất pt sau:

a, 4x-10<0

b, 2x+x+12\(\ge0\)

c, x-5\(\ge3-x\)

d, 7-3x>9-x

đ, 2x-(3-5x)\(\le4\left(x+3\right)\)

e, 3x-6+x<9-x

f, 2t-3+5t\(\ge\)4t+12

g, 3y-2\(\le2y-3\)

h,3-4x+24+6x\(\ge x+27+3x\)

i, 5-(6-x)\(\le4\left(3-2x\right)\)

k, 5(2x-3)- 4(5x-7)\(\ge19-2\left(x+11\right)\)

l, \(\dfrac{2x-5}{3}-\dfrac{3x-1}{2}< \dfrac{3-x}{5}-\dfrac{2x-1}{4}\)

m, \(5x-\dfrac{3-2x}{2}>\dfrac{7x-5}{2}+x\)

n, \(\dfrac{7x-2}{3}-2x< 5-\dfrac{x-2}{4}\)

Answer 1

[๖ۣۜĐặng♥๖ۣۜQuý]

a)

\(4x-10< 0\\ 4x< 10\\ x< \dfrac{10}{4}=\dfrac{5}{2}\)

b)

\(2x+x+12\ge0\\ 3x\ge-12\\ x\ge-\dfrac{12}{3}=-4\)

c)

\(x-5\ge3-x\\ 2x\ge8\\ x\ge4\)

d)

\(7-3x>9-x\\ -2>2x\\ x< -1\)

đ)

\(2x-\left(3-5x\right)\le4\left(x+3\right)\\ 2x-3+5x\le4x+12\\ 3x\le15\\ x\le5\)

e)

\(3x-6+x< 9-x\\ 5x< 15\\ x< 3\)

f)

\(2t-3+5t\ge4t+12\\ 3t\ge15\\ t\ge5\)

g)

\(3y-2\le2y-3\\ y\le-1\)

h)

\(3-4x+24+6x\ge x+27+3x\\ 0\ge2x\\ 0\ge x\)

i)

\(5-\left(6-x\right)\le4\left(3-2x\right)\\ 5-6+x\le12-8x\\ \\ 9x\le13\\ x\le\dfrac{13}{9}\)

k)

\(5\left(2x-3\right)-4\left(5x-7\right)\ge19-2\left(x+11\right)\\ 10x-15-20x+28\ge19-2x-22\\ 13-10x\ge-2x-3\\ -8x\ge-16\\ x\le\dfrac{-16}{-8}=2\)

l)

\(\dfrac{2x-5}{3}-\dfrac{3x-1}{2}< \dfrac{3-x}{5}-\dfrac{2x-1}{4}\\ \dfrac{40x-100}{60}-\dfrac{90x-30}{2}< \dfrac{36-12x}{60}-\dfrac{30x-15}{60}\\ \Rightarrow40x-100-90x+30< 36-12x-30x+15\\ 130-50x< 51-42x\\ 92x< -79\\ x< -\dfrac{79}{92}\)

m)

\(5x-\dfrac{3-2x}{2}>\dfrac{7x-5}{2}+x\\ \dfrac{10x}{2}-\dfrac{3-2x}{2}>\dfrac{7x-5}{2}+\dfrac{2x}{2}\\ \Rightarrow10x-3+2x>7x-5+2x\\ 12x-3>9x-5\\ 3x>-2\\ x>-\dfrac{2}{3}\)

n)

\(\dfrac{7x-2}{3}-2x< 5-\dfrac{x-2}{4}\\ \dfrac{28x-8}{12}-\dfrac{24x}{12}< \dfrac{60}{12}-\dfrac{3x-6}{12}\\ \Rightarrow28x-8-24x< 60-3x+6\\ 4x-8< -3x+66\\ 7x< 74\\ x< \dfrac{74}{7}\)

Answer 2

[qwerty]

a) \(4x-10< 0\)

\(\Leftrightarrow4x< 10\)

\(\Leftrightarrow x< \dfrac{5}{2}\)

b) ???

c) \(x-5\ge3-x\)

\(\Leftrightarrow2x-5\ge3\)

\(\Leftrightarrow2x\ge8\)

\(\Leftrightarrow x\ge4\)

d) \(7-3x>9-x\)

\(\Leftrightarrow7-2x>9\)

\(\Leftrightarrow-2x>2\)

\(\Leftrightarrow x< -1\)

đ) ???

e) \(3x-6+x< 9-x\)

\(\Leftrightarrow4x-6< 9-x\)

\(\Leftrightarrow5x-6< 9\)

\(\Leftrightarrow5x< 15\)

\(\Leftrightarrow x< 3\)

f) ???

g) ???

h) \(3-4x+24+6x\ge x+27+3x\)

\(\Leftrightarrow2x+27\ge4x+27\)

\(\Leftrightarrow-2x\ge0\)

\(\Leftrightarrow x\le0\)

i) \(5-\left(6-x\right)\le4\left(3-2x\right)\)

\(\Leftrightarrow5-6+x\le12-8x\)

\(\Leftrightarrow x-1\le12-8x\)

\(\Leftrightarrow9x-1\le12\)

\(\Leftrightarrow9x\le13\)

\(\Leftrightarrow x\le\dfrac{13}{9}\)

k) \(5\left(2x-3\right)-4\left(5x-7\right)\ge19-2\left(x+11\right)\)

\(\Leftrightarrow10x-15-20x+28\ge19-2x-22\)

\(\Leftrightarrow-10x+23\ge-3-2x\)

\(\Leftrightarrow-8x+13\ge-3\)

\(\Leftrightarrow-8x\ge-16\)

\(\Leftrightarrow x\ge2\)

l) \(\dfrac{2x-5}{3}-\dfrac{3x-1}{2}< \dfrac{3-x}{5}-\dfrac{2x-1}{4}\)

\(\Leftrightarrow-\dfrac{5}{6}x-\dfrac{7}{6}< -\dfrac{7}{10}x+\dfrac{17}{20}\)

\(\Leftrightarrow-\dfrac{2}{15}x-\dfrac{7}{6}< \dfrac{17}{20}\)

\(\Leftrightarrow-\dfrac{2}{15}x< \dfrac{121}{60}\)

\(\Leftrightarrow x>-\dfrac{121}{8}\)

m, n) làm tương tự:

đáp án: m. \(x>-\dfrac{2}{3}\); n. \(x< \dfrac{74}{7}\)