|2x-1/3-3x+1/5-x-2/15|leq5-2x/10 eching

$$| \frac { 2 x - 1 } { 3 } - \frac { 3 x + 1 } { 5 } - \frac { x - 2 } { 15 } | \leq \frac { 5 - 2 x } { 10 }$$

x uchun yechish

$$x\leq \frac{1}{2}$$

Qisqa yechim qadamlari

Tenglamaning ikkala tarafini 10 ga ko'paytirish. 10 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$10|\frac{2x-1}{3}-\frac{3x+1}{5}-\frac{x-2}{15}|\leq 5-2x$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 5 ning eng kichik umumiy karralisi 15. \frac{2x-1}{3} ni \frac{5}{5} marotabaga ko'paytirish. \frac{3x+1}{5} ni \frac{3}{3} marotabaga ko'paytirish.

$$10|\frac{5\left(2x-1\right)}{15}-\frac{3\left(3x+1\right)}{15}-\frac{x-2}{15}|\leq 5-2x$$

\frac{5\left(2x-1\right)}{15} va \frac{3\left(3x+1\right)}{15} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$10|\frac{5\left(2x-1\right)-3\left(3x+1\right)}{15}-\frac{x-2}{15}|\leq 5-2x$$

5\left(2x-1\right)-3\left(3x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$10|\frac{10x-5-9x-3}{15}-\frac{x-2}{15}|\leq 5-2x$$

10x-5-9x-3 kabi iboralarga o‘xshab birlashtiring.

$$10|\frac{x-8}{15}-\frac{x-2}{15}|\leq 5-2x$$

\frac{x-8}{15} va \frac{x-2}{15} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$10|\frac{x-8-\left(x-2\right)}{15}|\leq 5-2x$$

x-8-\left(x-2\right) ichidagi ko‘paytirishlarni bajaring.

$$10|\frac{x-8-x+2}{15}|\leq 5-2x$$

x-8-x+2 kabi iboralarga o‘xshab birlashtiring.

$$10|\frac{-6}{15}|\leq 5-2x$$

\frac{-6}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$10|-\frac{2}{5}|\leq 5-2x$$

a haqiqiy sonining mutloq qiymati qachon a\geq 0 bo‘lganda, a yoki qachon a<0 bo‘lganda -a. -\frac{2}{5} ning mutloq qiymati \frac{2}{5} ga teng.

$$10\times \frac{2}{5}\leq 5-2x$$

10\times \frac{2}{5} ni yagona kasrga aylantiring.

$$\frac{10\times 2}{5}\leq 5-2x$$

20 hosil qilish uchun 10 va 2 ni ko'paytirish.

$$\frac{20}{5}\leq 5-2x$$

4 ni olish uchun 20 ni 5 ga bo‘ling.

$$4\leq 5-2x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing. Bu imzo yo‘nalishini o‘zgartiradi.

$$5-2x\geq 4$$

Ikkala tarafdan 5 ni ayirish.

$$-2x\geq 4-5$$

-1 olish uchun 4 dan 5 ni ayirish.

$$-2x\geq -1$$

Ikki tarafini -2 ga bo‘ling. -2 manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x\leq \frac{-1}{-2}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-1}{-2} kasrini \frac{1}{2} ga soddalashtirish mumkin.

$$x\leq \frac{1}{2}$$