\(-4\frac{1}{2}\left(\frac{1}{2}-\frac{1}{6}\right)\le x\le\frac{-2}{3}.\left(\frac{1}{3}-\frac{1}{2}-\frac{3}{4}\right)\)

<=>  \(-1,5\le x\le\frac{11}{18}\)

đến đây tự làm

mk k biết điều kiện của x  nên giúp đến đó

\(\left(x+\frac{1}{2}\right)\left(x-\frac{3}{4}\right)=0\)

\(\Rightarrow\hept{\begin{cases}x+\frac{1}{2}=0\\x-\frac{3}{4}=0\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=-\frac{1}{2}\\x=\frac{3}{4}\end{cases}}\)

\(\left(x+\frac{1}{2}\right).\left(x-\frac{3}{4}\right)=0\)

\(x+\frac{1}{2}=0\)hoặc \(x-\frac{3}{4}=0\)

\(\Leftrightarrow x=-\frac{1}{2}\)hoặc \(x=\frac{3}{4}\)

\(\left(x+\frac{1}{2}\right).\left(x-\frac{3}{4}\right)=0\)

\(< =>\hept{\begin{cases}x+\frac{1}{2}=0\\x-\frac{3}{4}=0\end{cases}}\)

TH 1: \(x+\frac{1}{2}=0\)

\(x=0-\frac{1}{2}\)

\(x=-\frac{1}{2}\) (1)

TH 2: \(x-\frac{3}{4}=0\)

\(x=\frac{3}{4}+0\)

\(x=\frac{3}{4}\) (2)

Từ (1) và (2) => x thuộc tập hợp \(\left(-\frac{1}{2};\frac{3}{4}\right)\)

chúc bạn học tốt nha

\(4x-\left(x+\frac{1}{2}\right)=2x-\left(\frac{1}{2}x-5\right)\)

\(\Leftrightarrow4x-x-\frac{1}{2}=2x-\frac{1}{2}x+5\)

\(\Leftrightarrow4x-x-2x+\frac{1}{2}x=5-\frac{1}{2}\)

\(\Leftrightarrow\frac{3}{2}x=\frac{9}{2}\Leftrightarrow x=3\)

a.

\(\left(x+\frac{1}{2}\right)\times\left(x-\frac{3}{4}\right)=0\)

TH1:

\(x+\frac{1}{2}=0\)

\(x=-\frac{1}{2}\)

TH2:

\(x-\frac{3}{4}=0\)

\(x=\frac{3}{4}\)

Vậy \(x=-\frac{1}{2}\) hoặc \(x=\frac{3}{4}\)

b.

\(\left(\frac{1}{2}x-3\right)\times\left(\frac{2}{3}x+\frac{1}{2}\right)=0\)

TH1:

\(\frac{1}{2}x-3=0\)

\(\frac{1}{2}x=3\)

\(x=3\div\frac{1}{2}\)

\(x=3\times2\)

\(x=6\)

TH2:

\(\frac{2}{3}x+\frac{1}{2}=0\)

\(\frac{2}{3}x=-\frac{1}{2}\)

\(x=-\frac{1}{2}\div\frac{2}{3}\)

\(x=-\frac{1}{2}\times\frac{3}{2}\)

\(x=-\frac{3}{4}\)

Vậy \(x=6\) hoặc \(x=-\frac{3}{4}\)

c.

\(\frac{2}{3}-\frac{1}{3}\times\left(x-\frac{3}{2}\right)-\frac{1}{2}\times\left(2x+1\right)=5\)

\(\frac{2}{3}-\frac{1}{3}x+\frac{1}{2}-x-\frac{1}{2}=5\)

\(\left(\frac{1}{2}-\frac{1}{2}\right)-\left(\frac{1}{3}x+x\right)=5-\frac{2}{3}\)

\(-\frac{4}{3}x=\frac{13}{3}\)

\(x=\frac{13}{3}\div\left(-\frac{4}{3}\right)\)

\(x=\frac{13}{3}\times\left(-\frac{3}{4}\right)\)

\(x=-\frac{13}{4}\)

d.

\(4x-\left(x+\frac{1}{2}\right)=2x-\left(\frac{1}{2}-5\right)\)

\(4x-x-\frac{1}{2}=2x-\frac{1}{2}+5\)

\(4x-x-2x=\frac{1}{2}-\frac{1}{2}+5\)

\(x=5\)

\(2x-\frac{5}{4}=\left(3-\frac{1}{2}\right)\left(x-\frac{1}{3}\right)\)

\(\Leftrightarrow2x-\frac{5}{4}=\frac{5}{2}\left(x-\frac{1}{3}\right)\)

\(\Leftrightarrow2x-\frac{5}{4}=\frac{5x}{2}-\frac{5}{6}\)

\(\Leftrightarrow-\frac{x}{2}-\frac{5}{12}=0\)

\(\Leftrightarrow-\frac{x}{2}=\frac{5}{12}\Rightarrow-12x=10\)

\(\Rightarrow x=-\frac{5}{6}\)