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Penyelesaian - Linear inequalities with one unknown

Hasil Akhir Langkah-langkah Terma dan topik

m \geq - 8

m>=-8

Lihat langkah Learn more with Tiger Try this:

Penjelasan langkah demi langkah

1. Kumpulkan semua sebutan m di sebelah kiri ketaksamaan

$\frac{1}{2} \cdot m + \frac{2}{3} < = \frac{2}{3} m + 2$

Subtract $\frac{2}{3} m$ from both sides:

$(\frac{1}{2} m + \frac{2}{3}) - \frac{2}{3} \cdot m < = (\frac{2}{3} m + 2) - \frac{2}{3} m$

Kumpulkan sebutan sejenis:

$(\frac{1}{2} \cdot m + \frac{- 2}{3} \cdot m) + \frac{2}{3} < = (\frac{2}{3} \cdot m + 2) - \frac{2}{3} m$

Kumpulkan pekali:

$(\frac{1}{2} + \frac{- 2}{3}) m + \frac{2}{3} < = (\frac{2}{3} \cdot m + 2) - \frac{2}{3} m$

Cari penyebut sepunya terkecil:

$(\frac{(1 \cdot 3)}{(2 \cdot 3)} + \frac{(- 2 \cdot 2)}{(3 \cdot 2)}) m + \frac{2}{3} < = (\frac{2}{3} \cdot m + 2) - \frac{2}{3} m$

Darabkan penyebut:

$(\frac{(1 \cdot 3)}{6} + \frac{(- 2 \cdot 2)}{6}) m + \frac{2}{3} < = (\frac{2}{3} \cdot m + 2) - \frac{2}{3} m$

Darabkan pembilang:

$(\frac{3}{6} + \frac{- 4}{6}) m + \frac{2}{3} < = (\frac{2}{3} \cdot m + 2) - \frac{2}{3} m$

Gabungkan pecahan:

$\frac{(3 - 4)}{6} \cdot m + \frac{2}{3} < = (\frac{2}{3} \cdot m + 2) - \frac{2}{3} m$

Gabungkan pembilang:

$\frac{- 1}{6} \cdot m + \frac{2}{3} < = (\frac{2}{3} \cdot m + 2) - \frac{2}{3} m$

Kumpulkan sebutan sejenis:

$\frac{- 1}{6} \cdot m + \frac{2}{3} < = (\frac{2}{3} \cdot m + \frac{- 2}{3} m) + 2$

Gabungkan pecahan:

$\frac{- 1}{6} \cdot m + \frac{2}{3} < = \frac{(2 - 2)}{3} m + 2$

Gabungkan pembilang:

$\frac{- 1}{6} \cdot m + \frac{2}{3} < = \frac{0}{3} m + 2$

Permudahkan pembilang sifar:

$\frac{- 1}{6} m + \frac{2}{3} < = 0 m + 2$

Permudahkan aritmetik:

$\frac{- 1}{6} m + \frac{2}{3} < = 2$

2. Kumpulkan semua pemalar di sebelah kanan ketaksamaan

$\frac{- 1}{6} m + \frac{2}{3} < = 2$

Subtract $\frac{2}{3}$ from both sides:

$(\frac{- 1}{6} m + \frac{2}{3}) - \frac{2}{3} < = 2 - \frac{2}{3}$

Gabungkan pecahan:

$\frac{- 1}{6} m + \frac{(2 - 2)}{3} < = 2 - \frac{2}{3}$

Gabungkan pembilang:

$\frac{- 1}{6} m + \frac{0}{3} < = 2 - \frac{2}{3}$

Permudahkan pembilang sifar:

$\frac{- 1}{6} m + 0 < = 2 - \frac{2}{3}$

Permudahkan aritmetik:

$\frac{- 1}{6} m < = 2 - \frac{2}{3}$

Tukar nombor bulat kepada pecahan:

$\frac{- 1}{6} m < = \frac{6}{3} + \frac{- 2}{3}$

Gabungkan pecahan:

$\frac{- 1}{6} m < = \frac{(6 - 2)}{3}$

Gabungkan pembilang:

$\frac{- 1}{6} m < = \frac{4}{3}$

3. Asingkan m

$\frac{- 1}{6} m < = \frac{4}{3}$

Multiply both sides by inverse fraction $\frac{6}{- 1}$ :

Whenever you multiply or divide by a negative, reverse the inequality sign:

$(\frac{- 1}{6} m) \cdot \frac{6}{- 1} > = (\frac{4}{3}) \cdot \frac{6}{- 1}$

Kumpulkan sebutan sejenis:

$(\frac{- 1}{6} \cdot - 6) m > = (\frac{4}{3}) \cdot \frac{6}{- 1}$

Darabkan pekali:

$\frac{(- 1 \cdot - 6)}{6} m > = (\frac{4}{3}) \cdot \frac{6}{- 1}$

Permudahkan aritmetik:

$1 m > = (\frac{4}{3}) \cdot \frac{6}{- 1}$

$m > = (\frac{4}{3}) \cdot \frac{6}{- 1}$

Darabkan pecahan:

$m > = \frac{(4 \cdot - 6)}{3}$

Permudahkan aritmetik:

$m > = - 8$

4. Plot the solution on a coordinate grid

Solution:
$m \geq - 8$

Interval notation:
$[- 8, \infty]$

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Mengapa belajar ini

Learn more with Tiger

Inequalities help us understand how systems work by setting boundaries. For example, a speed limit of 30 miles per hour does not mean we have to drive exactly 30 miles per hour and, instead, establishes a boundary for what is allowable — drive more than 30 miles per hour and risk getting a ticket. This could be modelled mathematically as $x \leq 30$ .
There are also situations where there is more than one boundary. In our speed limit example, there may also be a lower speed limit of 15 miles per hour to prevent drivers from driving too slowly. The two boundaries together could be modelled mathematically as $15 \leq x \leq 30$ , in which $x$ represents all of the possible values between or equal to 15 and/or 30.

Furthermore, anytime we say something along the lines of, "it will take at least twenty minutes to get there," or "the car can hold five people at most," we are expressing the numerical boundaries of something and, therefore, speaking in terms of inequalities.

Terma dan topik

Linear inequalities

Penyelesaian - Linear inequalities with one unknown

Penjelasan langkah demi langkah

1. Kumpulkan semua sebutan m di sebelah kiri ketaksamaan

2. Kumpulkan semua pemalar di sebelah kanan ketaksamaan

3. Asingkan m

4. Plot the solution on a coordinate grid

Mengapa belajar ini

Terma dan topik

Pautan berkaitan

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