1/2x-1/6<1/3x+1/4 eching

$$\frac { 1 } { 2 } x - \frac { 1 } { 6 } < \frac { 1 } { 3 } x + \frac { 1 } { 4 }$$

x uchun yechish

$$x<\frac{5}{2}$$

Yechim qadamlari

Ikkala tarafdan \frac{1}{3}x ni ayirish.

$$\frac{1}{2}x-\frac{1}{6}-\frac{1}{3}x<\frac{1}{4}$$

\frac{1}{6}x ni olish uchun \frac{1}{2}x va -\frac{1}{3}x ni birlashtirish.

$$\frac{1}{6}x-\frac{1}{6}<\frac{1}{4}$$

\frac{1}{6} ni ikki tarafga qo’shing.

$$\frac{1}{6}x<\frac{1}{4}+\frac{1}{6}$$

4 va 6 ning eng kichik umumiy karralisi 12 ga teng. \frac{1}{4} va \frac{1}{6} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{6}x<\frac{3}{12}+\frac{2}{12}$$

\frac{3}{12} va \frac{2}{12} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{6}x<\frac{3+2}{12}$$

5 olish uchun 3 va 2'ni qo'shing.

$$\frac{1}{6}x<\frac{5}{12}$$

Ikki tarafini 6 va teskari kasri \frac{1}{6} ga ko‘paytiring. \frac{1}{6} musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$x<\frac{5}{12}\times 6$$

\frac{5}{12}\times 6 ni yagona kasrga aylantiring.

$$x<\frac{5\times 6}{12}$$

30 hosil qilish uchun 5 va 6 ni ko'paytirish.

$$x<\frac{30}{12}$$

\frac{30}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x<\frac{5}{2}$$