Question

tìm x biết :

a) \(\frac{1}{4}+\frac{1}{3}:2x=-5\)

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

c) \(\left|2x-3,5\right|=28\)

Answer 1

a.

\(\frac{1}{4}+\frac{1}{3}\div2x=-5\)

\(\frac{1}{3}\div2x=-5-\frac{1}{4}\)

\(\frac{1}{3}\div2x=-\frac{20}{4}-\frac{1}{4}\)

\(\frac{1}{3}\div2x=-\frac{21}{4}\)

\(2x=\frac{1}{3}\div\left(-\frac{21}{4}\right)\)

\(2x=\frac{1}{3}\times\left(-\frac{4}{21}\right)\)

\(2x=-\frac{4}{63}\)

\(x=-\frac{4}{63}\div2\)

\(x=-\frac{4}{63}\times\frac{1}{2}\)

\(x=-\frac{2}{63}\)

b.

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

TH1:

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

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

\(x=-\frac{1}{4}\div3\)

\(x=-\frac{1}{4}\times\frac{1}{3}\)

\(x=-\frac{1}{12}\)

TH2:

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

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

Vậy \(x=-\frac{1}{12}\) hoặc \(x=-\frac{1}{2}\)

c.

\(\left|2x-3,5\right|=28\)

\(2x-3,5=\pm28\)

TH1:

\(2x-3,5=28\)

\(2x=28+3,5\)

\(2x=31,5\)

\(x=31,5\div2\)

\(x=15,75\)

TH2:

\(2x-3,5=-28\)

\(2x=-28+3,5\)

\(2x=-24,5\)

\(x=-24,5\div2\)

\(x=-12,25\)

Vậy \(x=-12,25\) hoặc \(x=-15,75\)

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