Simplify: 1/2(4x+4) − 1/5(x+5)

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19. St. Paul Junior school organized a tour for candidate class to Jinja which is 240km away. After covering $\frac{2}{5}$ of the journey, candidates were taken for breakfast. Work out the distance which was remaining to reach Jinja.

Tambua umbali wote wa safari.
Umbali wote ni $240 \text{ km}$ .
Hesabu sehemu ya safari iliyobaki.
Ikiwa $\frac{2}{5}$ ya safari imefunikwa, basi sehemu iliyobaki ni $1 - \frac{2}{5}$ .
$1 - \frac{2}{5} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5}$
Hesabu umbali uliosalia kufika Jinja.
Umbali uliosalia = Sehemu iliyobaki $\times$ Umbali wote
$\text{Umbali uliosalia} = \frac{3}{5} \times 240 \text{ km}$ $\text{Umbali uliosalia} = 3 \times \frac{240}{5} \text{ km}$ $\text{Umbali uliosalia} = 3 \times 48 \text{ km}$ $\text{Umbali uliosalia} = 144 \text{ km}$
Jibu la mwisho ni:
$\boxed{144 \text{ km}}$
20. Simplify: $\frac{1}{2}(4x + 4) - \frac{1}{5}(x + 5)$
Panua (distribute) nambari za nje kwenye mabano.
$\frac{1}{2}(4x + 4) = \left(\frac{1}{2} \times 4x\right) + \left(\frac{1}{2} \times 4\right) = 2x + 2$ $\frac{1}{5}(x + 5) = \left(\frac{1}{5} \times x\right) + \left(\frac{1}{5} \times 5\right) = \frac{1}{5}x + 1$
Andika upya mlinganyo kwa kutumia matokeo ya upanuzi.
Kumbuka kutoa nambari zote za pili.
$(2x + 2) - \left(\frac{1}{5}x + 1\right)$ $2x + 2 - \frac{1}{5}x - 1$
Panga upya maneno yanayofanana pamoja.
$2x - \frac{1}{5}x + 2 - 1$
Unganisha maneno yanayofanana.
Kwa maneno ya $x$ :
$2x - \frac{1}{5}x = \frac{10}{5}x - \frac{1}{5}x = \frac{9}{5}x$
Kwa maneno ya nambari:
$2 - 1 = 1$
Andika jibu lililorahisishwa.
$\frac{9}{5}x + 1$
Jibu la mwisho ni:
$\boxed{\frac{9}{5}x + 1}$

Simplify: 1/2(4x+4) - 1/5(x+5)

Answer

Step-by-step solution

Tambua umbali wote wa safari.

Hesabu sehemu ya safari iliyobaki.

Hesabu umbali uliosalia kufika Jinja.

Panua (distribute) nambari za nje kwenye mabano.

Andika upya mlinganyo kwa kutumia matokeo ya upanuzi.

Panga upya maneno yanayofanana pamoja.

Unganisha maneno yanayofanana.

Andika jibu lililorahisishwa.

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